Preheat oven to 350 degrees F (175 degrees C). Coat a baking sheet lightly with cooking spray.
Heat a large skillet over medium heat. Add sausage; cook and stir until browned, 5 to 7 minutes. Remove sausage, reserving some of the grease. Add flour to the skillet and mix well. Stir in milk; season gravy with salt and pepper. Remove from heat.
Separate biscuits and arrange side-by-side onto the prepared sheet. Press down biscuits to seal them together into a crust that covers the whole sheet.
Bake in the preheated oven until crust is very lightly browned, about 5 minutes. Remove crust from oven and keep oven on. Press crust to flatten.
Heat butter in a large nonstick skillet over medium heat until the foam disappears, about 2 minutes. Pour in eggs; cook and stir with a spatula until eggs are set but still moist, 3 to 4 minutes. Arrange eggs on the crust. Top with the sausage and gravy. Spread Cheddar cheese and mozzarella cheese over the pizza. Season with salt and pepper.
Bake on the top rack of the hot oven until cheeses are bubbling and top begins to brown, about 10 minutes.