One-Note Cook

A character—frequently male—who is only able to make one specific kind of food, often because they're a Lethal Chef and attempts to diversify their efforts would end in disaster. Through harsh training, they have finally become able to make one thing that is edible, at least. If it's their Trademark Favourite Food, they're in luck.

Sometimes Truth in Television—it's relatively common for people who aren't particularly good at cooking (even if they're not quite at Lethal Chef levels) to be able to make a few dishes fairly well.

Examples of One-Note Cook include:

Anime and Manga

Shana of Shakugan no Shana only makes melonpan, and packs her lunchbox full of it. Then again, it's her signature food, so she probably doesn't care, and her guardian, Wilhelmina, was a far worse Lethal Chef.
Nerine of SHUFFLE! can't cook, but after taking cooking lessons, she is able to make omelets (and only omelets) for lunch, in large quantities. Before she took lessons, her cooking attempts usually resulted in explosions and something worse, so when she finally learned how to cook omelets her dad wanted to create a holiday to celebrate.
Revolutionary Girl Utena's Anthy sticks to shaved ice. Any other meal she cooks up tend to have very interesting side-effects, which may or may not be intentional.
Saati in A.I. Love You, after learning to cook, can only make curry, even when she tries to make something else.
This is practically a plot point of Yakitate!! Japan.
- Considering the sheer variety of bread Azuma can make, this might also fall under When All You Have Is a Hammer.
Akane Tendo of Ranma ½ is a Lethal Chef, but it's said that when she really tries her curry is bearable, "Maybe... even tasty."
- Ukyou, who is otherwise considered a Supreme Chef, rarely bothers cooking anything that isn't okonomiyaki. To the point that when she tried to give it up, she suffered withdrawal symptoms and ended up cooking Ranma like an okonomiyaki.
One episode of Sailor Moon has Usagi trying to cook and failing badly...until she makes curry, which Mamoru and Chibi-Usa both enjoy, the latter even asking "Can we have this every night?" In the rest of the series she's a Lethal Chef - especially when it comes to curry.
Tohno Shiki from Tsukihime is good at making noodles.
Inverted in Kanon where Akiko can make everything, except a Special Jam which can file her under Lethal Chef.
In Kannagi, Tsugumi enjoys cooking. She can make eggs, vegetables, and eggs with vegetables.
Nana's mother in Nana to Kaoru can make rice omelette. Just rice omelette. It's still a step up from her daughter.
Haruna in Kore wa Zombie Desu ka? can only make fried eggs... but they're really good fried eggs.
Ringo Oginome of Mawaru Penguindrum starts the series only being able to make curry, but learns how to cook more things under Himari, Shouma and Kanba's tutelage. It also serves a metaphor for her Character Development, since curry represents her clinging to her past, and specifically the memory of her dead older sister Momoka.

Film

The remake of The Parent Trap has the father offer to make dinner for his ex-wife. She's surprised that he's learned to cook. It turns out he can make "pasta...or pasta...or pasta." She plays along and says "the pasta sounds good."
The older brother in Zathura can make one thing: water.
Riggs in Lethal Weapon only knows how to make chili.

Riggs: Do you like your chili with or without crushed Oreos?
Rika: With, of course!
Riggs: Heh heh. Woman after my own heart.

Literature

In James Herriot's All Things Wise And Wonderful, kitchen duties are temporarily taken over by Tristan Farnon, who can only cook sausage and mash - and even that not always particularly well.
- His fire-lighting technique needed some work too.
Albert, The Grim Reaper's manservant in Discworld novels, can only make fry-ups. He will experiment with porridge or Hogswatch pudding, but only by frying them. Fortunately, Death doesn't need to eat.
- It should be noted that it's not that Albert can't make anything un-fried, it's that he can't wrap his brain around un-fried food, since that's all he ever eats. The fried porridge thing was considered progress.
  - If porridge is a mixture of oatmeal, milk and water then by adding yeast, letting it work for an hour and then frying it you get Staffordshire Oatcakes, which are more than respectable food.
- He did manage a mug of cocoa once. Well, he was close. If you turned the mug sideways, it would pour out eventually.
- Lady Sybil Vimes can similarly only do a fry-up, and that's usually frazzled. Fortunately, years as a street copper have resulted in Sam Vimes actually preferring greasy, frazzled food.
Something of a reversal, rather than only making one dish, the cook in Alice in Wonderland seems to think the only ingredient is pepper. It isn't elaborated whether or not she is actually able to make anything out of this or not, but given that its Alice in Wonderland it is definitely possible.

Live-Action TV

In Friends, Rachel can only make good brownies.
In How I Met Your Mother, Lily tells Marshall how delicious his pancakes are and ask if he would like to make dinner sometime. He responds "Sure... how about pancakes?"
In the sitcom Alice, Mel's cooking is routinely slammed - even by his regular customers (curious for a diner that's apparently been running for years). Yet, he apparently makes a mean chili. (It sneaks in as a plot point in several episodes.)
Lois and Clark: "I can only make 4 things, and this is the only one without chocolate..."
Charlie from Two and A Half Men tries to learn to cook. He asks everyone how they want their eggs, and no matter what the answer is, he responds "Scrambled it is."
Debra from Everybody Loves Raymond can only cook Lemon Chicken. Everything else is disgusting. There was an episode titled "Debra Makes Something Good" where she makes Brajole. However, she stops making it after that episode.
When he travels back in time, the grown Hiro Nakamura is mistaken by his father to be the new chef (the Hiro of that time was a young boy). His mother orders eggs... but all Hiro knows how to make is waffles. She isn't mad at him.
Mistress Ploppy in Blackadder II, who prepares whatever the condemned prisoners want for their final meal. As long as they want sausages.

Newspaper Comics

Calvin's Dad in Calvin and Hobbes

Calvin's Dad: Since your mom's sick, I'm making dinner tonight.
Calvin: You can cook?
Calvin's Dad: As you can see, I survived two years of my own cooking when I had an apartment after college.
Calvin: Mom says you ate frozen waffles and canned soup three times a day.
Calvin's Dad: Your mom wasn't there, so she wouldn't know. Get the syrup out, will you?

Video Games

C-Sha in Megadimension Neptunia VII is a great cook of roast meat. Unfortunately, that seems to be the only thing she can cook.
Minori in the game Brass Restoration can make rice, and pure evil.
Somewhat of an example with Lethal Chef Raine in Tales of Symphonia, gameplay-mechanics-wise. Her cooking skill for almost all of the recipes in the game max out at two stars (for most characters, that only applies to a few recipes they happen to be "bad" at). However, her ability to cook spaghetti is better than that for the other recipes... that one maxes out at three stars. (And she starts out with one star on that recipe, instead of starting with zero stars for all the other recipes.)
Flora of the Harvest Moon series is a Lethal Chef for anything that isn't curry. She knows it, hence it's all she cooks. Unfortunately for her, this has resulted in her boss/love interest Carter being sick to death of the stuff.
Chef Shimi from Paper Mario: The Thousand-Year Door can cook only with mushrooms, though he is stated to be a pretty good cook by NPCs.
Snake and Otacon's daughter, Sunny, is incapable of cooking anything but eggs. Justified in that she also lives in an airplane and presumably subsists entirely on military-style rations and eggs from the three chickens on the plane. At one point, she attempts to cook a block of ramen in the same manner as fried eggs (by plopping it in a frying pan), and ends up setting a fire.
Atelier Annie has Gillian, who attempts to put herbal health drinks in everything. Unfortunately for the rest of the world, she and Melody are the only people who can even get near said herbal health drinks without gagging.
Papyrus from Undertale is memetically associated with pasta, as it is the only food he seems to cook in the game (though a throwaway line implies that he at least knows how to make quiche and Word of God stated that pasta isn't his actual favorite food despite his fondness to make it). Too bad he is also a legendarily bad cook and his spaghetti dishes are completely inedible.
- Undyne, who is just as bad a cook as Papyrus above, is noted to be capable of brewing a surprisingly good cup of tea (even if she serves it way too hot).

Web Comics

The company chef in Schlock Mercenary only makes things that involve whisking. Presumably because he has a whisk for a prosthesis.

Western Animation

In Mickey Tries To Cook, Minnie berates Mickey for only being able to make Cheese Ham and Tomato sandwiches, and thus that's all they ever eat at picnics. Mickey's attempts to learn how to cook something else ends in disaster.
Arguably SpongeBob SquarePants. When he trades places with a chef for a fancy restaurant, his attempts at haute cuisine ends up turning into Krabby Patties.
- An early episode showed him as having no idea what a sa-lad was. When he learned, the concept of tomatoes and lettuce without a bun and patty freaked him out.
In A Charlie Brown Thanksgiving, Charlie Brown expresses (and demonstrates) an inability to make anything other than cold cereal "and maybe toast". He serves cold cereal again in Race for Your Life, Charlie Brown, (though apparently no one else even thought to bring food on their river-raft expedition).
In an episode of Venture Brothers, Sergeant Hatred takes over Hank's greasy spoon diner he's opened on the family compound, but admits that he only knows how to make scrambled eggs with ketchup.
Doug and maybe by extension his entire family, have several books on making grill cheese sandwiches. That suggests Doug can make mean cheese sandwiches.
Manjula from The Simpsons; one of her talents is cooking a wide variety of dishes using only chickpeas, lentils, and/or rice

Real Life

Although not that common in the U.S., many countries with a strong culture of cheap outside dining will have cooks who are extremely good at making things like tacos, pancakes, noodles, etc. These same cooks may also be absolute shit at cooking anything else, sometimes not even being able to cook their own meals aside from their specialty.
Chef Duff from Ace of Cakes subverted this when he performed on Iron Chef America, and made excellent food. He still lost to Michael Symon, though.
Bobby Flay gets accusations of this. While he's usually not abysmal at cooking outside of his element, his style heavily leans on usage of hot peppers - you can practically predict how close of a match he'll have in Iron Chef or Throwdown based on how well the secret ingredient/proposed dish would work with spicy peppers thrown in.