Divide the butter among five 13x9-in. baking dishes; set aside. In a large bowl, beat 20 eggs, 2 cups milk and 1/4 teaspoon pepper until blended. Stir in 1-1/2 cups cheese and 1-1/2 cups ham; pour into one prepared dish. Repeat four times.
Bake, uncovered, at 350° for 40-45 minutes or until a knife inserted in the center comes out clean (cover with foil if the top browns too quickly). Let stand for 5 minutes before cutting.