Are there restaurants that have a duck egg-centric breakfast menu?
Lots of places have poached duck eggs, and many of those even offer them for breakfast.
But I'm looking for a place that will offer duck eggs in the full array of breakfast dishes.
Scrambled duck eggs
Duck egg omelet
Fried duck egg
French toast (made with duck eggs)
Duck eggs Benedict
Basically similar to one of JoeDoe's dishes - duck hash with duck eggs. JoeDoe's is one of the best duck hashes in the city, IMHO. The little vinegary slaw it comes with is a perfect counterbalance to the richness of the rest of the dish.
Also, you can buy duck eggs nearly anywhere in Chinatown, and cook them however you like at home.
I wouldn't personally make French Toast with duck eggs - the whites don't really fluff up enough, they're much thinner than in other eggs. You wouldn't get that custardy texture. Chicken eggs are much better for that kind of application.