Frittatas, omelettes, Spanish tortillas, obviously. Angel food cake, fruit curd. What else?
sabayon (zabaglione)...creme caramel/flan...quiche...matzoh brei...
Souffles and macarons
Perhaps you should define what you mean by lots of eggs. A standard recipe for avgolemono soup serving four calls for three eggs--less than one egg per person. Kaiserscharrn (also serving four), a fluffy pancake served with fruit compote calls for 4 whole eggs plus 12 whites--a lot of eggs, but when you get down to it, not many yolks.
Avgolemono is the best. Put that at the top of the list.
Another dish to keep the hens happy: oeufs a la neige.
chilaquiles, huevos rancheros, a poached egg on top makes anything taste better! We put boiled eggs on salads, and who doesn't love an egg salad sandwich?
Chawanmushi or gaeran jim: savory steamed egg custard
More egg-centric foods:
Eggs en cocotte
Genoise (sponge cake)
French Buttercream frosting
Zuppa Inglese or English Trifle
Ice cream uses a lot of yolks. Paired with meringue cookies it is great way to use up eggs. I also love alice medrich's chocolate mousse recipes that use eggs instead of dairy.