Heat a large skillet over medium heat. Cook and stir sausage in the hot skillet until browned, 5 to 7 minutes. Drain and discard grease. Stir in flour until dissolved; add 2 cups milk. Stir occasionally until gravy reaches desired consistency, about 10 minutes. Season gravy with black pepper.
Preheat oven to 400 degrees F (200 degrees C).
Place pizza crust on a baking sheet; brush with olive oil. Spread 1/2 of the gravy over the olive oil.
Spray a large skillet with cooking spray; warm over medium-high heat. Whisk eggs and 1/4 cup milk together in a bowl. Pour into the skillet; cook and stir until eggs are set, about 5 minutes.
Top pizza with scrambled eggs and Cheddar cheese.
Bake in the preheated oven until crust is golden brown and top is bubbling, 10 to 15 minutes.