Generously grease a 9x13-inch glass baking dish with softened butter. Stir together flour and mustard powder. Place ham and Cheddar cubes in a large mixing bowl, sprinkle with flour mixture, and toss until evenly coated. Add bread cubes and toss to mix. In a separate bowl, whisk together eggs, milk, and hot pepper sauce.
Pour 1/3 of the bread mixture into the prepared baking dish and smooth out to form a layer. Drizzle with 1 tablespoon of butter, and sprinkle with 1/3 of the Parmesan cheese. Repeat twice more to form three layers. Pour egg mixture overtop, cover with plastic wrap, and refrigerate 8 hours to overnight.
The next morning, remove casserole from refrigerator, remove plastic wrap, and allow to stand at room temperature for 30 minutes. Preheat oven to 350 degrees F (175 degrees C).
Bake uncovered in preheated oven until the eggs have set, and the top is golden brown and crispy, about 1 hour.