Lay half of the bread slices on your work surface, spread with the mustard and evenly distribute the ham and cheese. Top with the remaining bread slices.

Heat a griddle or nonstick pan over medium-low heat, and brush with the butter.

Cook the sandwiches on the first side until golden brown and crisp. Flip, adding more butter if necessary, and continue to cook until the cheese is melty.

Preheat the broiler to medium.

Transfer the sandwiches to a parchment-lined sheet tray, and top with Béchamel sauce. Broil the sandwiches until the Béchamel is bubbly and golden brown.

Cut the sandwiches in halves or quarters, and serve while hot.