dont know if you would call it an egg bake or not but many years ago dad came up with a creation I still make a couple of times a year.
while your oven is preheating to 350,in a large skillet,add one tablespoon of pure olive oil,saute a chopped small onion,one clove of garlic,one each chopped red and yellow bell peppers.
remove the skillet from the heat when done with the saute
slice up a ring of bologna and add it to the mix.
whip six or eight eggs and pour them over the mix in the skillet and place the skillet in the oven.
when the eggs are starting to just slightly brown up add your favorite shredded cheese and bake until cheese is melted.