In a large bowl, mix bread, ham, and cheese cubes.

Place 1/3 of the mixture in a 9 x 13-inch baking dish.

Mix flour and dry mustard in a cup.

Sprinkle 1 tablespoon of the flour mixture over the bread mixture in the baking dish.

Drizzle with 1 tablespoon of melted butter over the bread mixture.

Repeat the layering process with the remaining bread mixture, flour mixture, and butter to create 2 more layers.

In a separate bowl, beat the eggs and milk until foamy.

Pour the egg mixture evenly over the layers in the baking dish.

Cover the baking dish.

Chill in the refrigerator for at least 4 hours, or preferably overnight.

Preheat the oven to 350°F (175°C).

Bake, uncovered, for 1 hour, or until the casserole is golden brown and puffed.