In a large bowl, combine the broccoli, ham and cheese; spread half into a greased 13-in. x 9-in. baking dish. Arrange bread slices on top. Cover with remaining broccoli mixture. In a large bowl, combine the eggs, milk, onion, mustard and hot pepper sauce. Pour over broccoli mixture. Sprinkle with paprika. Cover and refrigerate overnight.
Remove from the refrigerator 30 minutes before baking. Bake, uncovered, at 350° for 35-40 minutes or until a knife inserted near the center comes out clean. Let stand for 5 minutes before serving. Yield: 12 servings.