Cut the crusts off of the bread and cut each slice in half. Arrange half of the bread in the bottom of the dish. Top with half of the ham and half of the cheeses.
Repeat with the remaining bread, ham, and cheese.
In a large bowl, whisk together the eggs, milk, onion powder, and dry mustard. Pour the mixture over the bread. Cover and refrigerate overnight.
When you're ready to bake it, preheat oven to 375 F. Remove the dish from the refrigerator and uncover.
In a medium bowl, stir together the corn flakes and melted butter. Sprinkle this mixture over the casserole and bake for 55 to 65 minutes, or until the center barely jiggles when you shake the pan.