In a large bowl, combine the broccoli, ham and cheese; spread half the mixture into a greased 13x9x2-inch baking dish. Arrange bread slices on top and cover with remaining ham//cheese/broccoli mixture. In a large bowl, combine the eggs, milk, onion flakes, mustard and hot pepper sauce. Pour over broccoli mixture. Sprinkle with paprika. Cover and refrigerate overnight.
Remove from the refrigerator 30 minutes before baking, uncovered, for 35-40 minutes or until a knife inserted in the center comes out clean. Let stand 5 minutes before serving.