Melt butter in 13x9-inch baking dish. Place cubed bread to cover bottom of dish. Sprinkle cheese over bread cubes. Sprinkle diced ham over cheese. Beat eggs with milk. Pour over casserole. Cover tightly with foil and refrigerate over night.
When ready to bake, preheat oven to 375 degrees. Bake covered for 20 minutes; remove foil and continue to bake for 10-15 minutes or until lightly browned and puffy. Serve immediately.