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.
Assemble sandwiches:
Preheat oven to 400° 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.
Top a slice of bread with a piece of ham, gruyere, and a sprinkle of parmesan cheese. Place another slice of bread on top, béchamel side up, then top with remaining gruyere and parmesan cheese. repeat for remaining sandwiches.
Bake in the oven 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.