Spray a 9×13-inch casserole dish with cooking spray.
Spread ham into the bottom of prepared casserole dish. Butter one side of each bread slice; cut slices into cubes. Arrange buttered bread cubes atop ham; layer American cheese over bread cubes.
Whisk milk, eggs, mustard powder, and salt together in a bowl; pour over American cheese layer. Cover dish with aluminum foil and refrigerate 8 hours or overnight.
Preheat oven to 350 degrees F (175 degrees C). Remove aluminum foil from casserole.
Bake in the preheated oven until cheese is melted and eggs are set in the middle, about 1 hour.