Chop half of the bread into 1/2-inch pieces. In a bowl, toss with the melted butter.
Spread mustard over remaining bread and arrange, overlapping slightly, in a greased 2-qt. baking dish. Sprinkle 1/2 cup of cheese on top. Fold ham slices in half and arrange in an even layer over bread. Top with half of remaining cheese. Sprinkle with the chopped bread and remaining cheese.
In a bowl, whisk the eggs and milk; season. Pour over the casserole and let stand at room temperature for 30 minutes.
Position a rack in the upper third of oven; preheat to 400 degrees . Bake until casserole puffs and top is golden-brown, about 30 minutes. Let cool for 5 minutes before serving.