Cook the sausage and onion in an oven-proof skillet over medium heat until the sausage has browned, about 10 minutes. Drain excess grease from the skillet. Whisk together the eggs, milk, sour cream, salt, and pepper. Sprinkle the sausage with 1 cup of the Cheddar cheese, then pour the egg mixture overtop.
Bake in the preheated oven until a knife inserted into the center comes out clean, about 18 minutes. Sprinkle with the remaining Cheddar cheese, and return to the oven until the cheese has melted. Cut into wedges to serve.