Preheat the oven to 375°F. Generously grease an 8-inch square baking dish with nonstick spray. Line a baking sheet with foil.
In a blender, combine the eggs, cottage cheese, salt, and pepper. Blend until uniform and frothy, about 5 seconds. Pour into the prepared baking dish. Bake until the eggs are just set, 20-25 minutes. Remove from the oven and turn the oven to broil.
Separate the bottom and top halves of the buns, otherwise leaving the individual buns intact, then place cut-side up on the prepared baking sheet. Broil until toasted, 1 to 3 minutes.
Run a knife around the perimeter of the eggs to loosen, then carefully transfer onto the bottom halves of the buns. Place in the baking dish and top with the cheese. Broil until the cheese is melted, about 1 minute.
Drizzle with hot sauce, if using, then cover with the top halves of the buns. Cut into individual sliders before serving.
