Nobody Dies: The Yomiverse

An alternate timeline to Nobody Dies, where Kei Ayanami ran away rather than face her family in the aftereffects of the Zeruel fiasco. Given that she, in fact, only really knows one person who isn't closely related to her, she ends up in Germany with Kaworu Nagisa, her boyfriend, estranged from Yui and the rest of her family.

The inevitable happens.

And eventually they end up with a healthy, cheerful, sometimes squamous and rugose, israfim-eating... Eldritch Abomination, who they called Yomiko. Her grandparents are ADAM, Lilith, Yui Ikari, and Kihl Lorenz. And despite that, she is remarkably normal. Normal-ish.

K 9 Thefirst 1 came upwith the idea, and as of January 2011 there is only one chapter of the main plot. Gregg Landsman has also written a future, where a Fourteen year-old Yomiko is reunited with her family. The fans are speculating one how much of it is canon and how much was for kicks and giggles.

However, the most work has been done by EarthScorpion's "Little Yomiko" shorts, that apply Moe to an almost Science-based Addams Family environment with the Nagisas. The Yomiko Absolution covers the revelation of Yomiko's family past, and her subsequent adventure to Tokyo-3, strictly against her mother's rules.

Individuals are also advised to refer to Nobody Dies for other tropes which may appear.
 * Spin Offspring: The central character is Yomiko Leliel Nagisa, the daughter of Kei and Kaworu. In addition, Ariel Ikari-Soryu (Asuka and Shinji's), and Aiko Ayanami (Hatchi's) have also appeared, and there is the solid implication that there are more progeny out there.