Cook sausage in a large skillet over medium heat until browned, breaking it up with a spoon. Drain off excess grease.
In the same skillet, whisk together flour and milk until smooth. Bring to a simmer, stirring constantly, until thickened. Stir in salt and pepper to taste.
Remove from heat and stir in half of the cheddar cheese.
Separate the biscuit dough into individual biscuits and place them on a baking sheet to form the pizza crust. Slightly flatten each biscuit.
Pour the sausage gravy evenly over the biscuit crust. Top with remaining cheddar cheese and bake for 15-20 minutes, or until golden brown and bubbly.
In a separate pan, scramble the eggs with butter until cooked through.
Top the baked pizza with the scrambled eggs and serve immediately.
Notes
For a spicier kick, use hot Italian sausage. You can also add other vegetables like bell peppers or onions to the gravy.