Melt butter in a medium saucepan over medium heat. Whisk in flour and cook, stirring constantly, for about 3 minutes. Gradually add milk, stirring well until the mixture is smooth. Cook, stirring, until sauce is thickened. Season with a little bit of salt and pepper. Remove from heat and whisk in mustard and nutmeg. Set aside while you make the sandwiches, or make the sauce up to 1 week in advance.

Preheat oven to 425° F. Line a baking tray with parchement paper and set aside.

Spread each bread slice with a layer of béchamel, spreading it all the way to the edges. Place 4 slices of bread, béchamel side up, on prepared baking sheet. Top each with a piece of ham, a handful of gruyere, and a sprinkle of parmesan cheese. Place remaining slices of bread on top, béchamel side up, then top with remaining gruyere and parmesan cheese.

Bake at 425 degrees F for about 5-6 minutes, until cheese is melted, and then turn the oven to broil and broil until the cheese on top is lightly golden, 2-4 minutes.