Preheat oven to 350°F. Grease or spray 9 x 13 baking pan with non-stick cooking spray.
In a large skillet, cook sausage and onion until onion is softened and beginning to brown, and sausage is cooked through. Stir frequently, breaking up any sausage chunks while it cooks. Remove from heat and set aside.
In a large mixing bowl, whisk together eggs, milk, paprika, butter, salt and pepper until well combined. Add the cheese, sausage, onions, and hominy and stir well.
Pour mixture into prepared dish and sprinkle with more cheese if desired. Bake uncovered for about 1 hour or until edges are browned and a tester comes out clean. Let stand for about 10 minutes before serving. Enjoy!