How to Make It
Preheat oven to 400°F. Lightly coat a large rimmed baking sheet with non-stick spray, line with parchment, and spray again. Place eggs in a blender and process until evenly combined; season with salt and pepper.
Pour eggs into prepared baking sheet and carefully transfer to oven. Bake until barely set in the middle, 10 to 12 minutes. Remove eggs from oven and top with cheese.
Heat broiler to high and return eggs to oven. Broil until cheese is just melted, about 1 minute.
Cut eggs into 12 squares. Lightly butter rolls or buns and build sandwiches with egg squares, bacon, and hot sauce or ketchup.