Preheat oven to 350°F. Grease or spray 9 x 13 baking pan with non-stick cooking spray.
In a large skillet, cook sausage until no pink remains, breaking up any chunks as it cooks. Drain fat as needed.
In a large mixing bowl, stir together sausage, 1 1/2 cups cheese and hominy. Whisk together eggs, milk, paprika and pepper. Stir in butter until combined. Stir egg mixture into sausage mixture until well combined.
Transfer mixture to prepared pan and sprinkle with remaining cheese. Bake uncovered for about 1 hour or when knife inserted in center comes out clean. Let stand for 5 minutes before serving.
Store any leftovers tightly covered in the refrigerator for up to 3 days.