Preheat the oven to 400 degrees.

In a small saucepan, melt the butter over low heat and add the flour, stirring constantly for 2 minutes.

Add the hot milk, slowly, and whisk until the sauce has thickened.

Turn the heat off and add the salt, pepper, nutmeg and cheese (1/2 cup of the Gruyere and Parmigiano Reggiano).

Lightly brush one side of each bread with Dijon mustard.

Add Gruyere cheese to each side, one slice of ham and then close the sandwiches together.

Spoon the bechamel sauce on top of the sandwiches and then sprinkle the rest of the Gruyere cheese.

Bake the sandwiches for 5 minutes.

Turn on the broiler and broil the sandwiches until the top is bubbly and slightly browned.

Serve warm.