Cut half of the bread into ½ inch pieces. Place in large bowl and pour melted butter over it and stir until bread is moistened.
Spread Dijon mustard on the remaining slices of bread. Lay the bread on bottom of greased casserole dish. If you need to, overlap pieces. Sprinkle ½ cup of cheese on top of bread. Fold slices of ham in half and layer evenly on top of cheese. Sprinkle ½ of the remaining cheese over the ham. Cover all with the chopped pieces of bread and then with remaining cheese.
Mix together eggs, milk, and a pinch of salt and pepper. Pour over the casserole and let stand at room temperature for 30 minutes to an hour.
Preheat oven to 400 degrees. Bake until lightly brown and bubbly on top, about 25-35 minutes. Let cool for at least 5 minutes before serving. Serve with your favorite syrup on the side.