Preheat your oven to 400°F (200°C).
Spread half of the béchamel sauce on one side of each slice of bread.
Spread Dijon mustard on the other side of each slice.
Layer the ham and half of the Gruyère cheese on top of the béchamel side of one slice of bread, then place the other slice of bread on top, béchamel side down.
Spread half the butter on the outside of the sandwich, then sprinkle with the remaining Gruyère cheese.
Place the sandwich on a baking sheet and bake in the preheated oven for 10 minutes, or until the cheese is melted and the bread is golden brown.
Remove from the oven, cut in half, and serve hot.