Los Anaya will make the chilaquiles with fried/over easy egg if you request it! I asked only after I had mine because I wanted to try their version for my first go, but next time, I will get it with an over easy egg + double sour cream, I think omitting the guac.
Egg yolk + chilaquiles is just utterly glorious.
However, Los Anaya makes such great huevos rancheros...unparalleled imo. I think their fresh corn tortillas rival almost anything I've had in Mexico (except maybe for the tortillas at places like Quintonil and Pujol, but that seems unfair as a comparison). There is something truly remarkable about the fluffiness and chewiness that is just perfect with the egg yolks and their ranchera sauce (and diablo sauce)...particularly with their rice and beans (the rice being rather Americanized I think? But it tastes remarkably good).