Combine the egg and milk in a shallow dish and whisk until blended. Combine the onions and cheese, bread crumbs, paprika, salt and pepper in a shallow dish and mix well. Dip the chicken in the the egg mixture. Roll in the bread crumb mixture to coat.
Arrange the chicken in a 9x12 inch baking dish and drizzle with the butter. Bake at 350 degrees F for 45 minutes to 60 minutes, or until the chicken registers 165. Refrigerate any leftovers.