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 salt and pepper to taste. Whisk in mustard and nutmeg, then remove from the heat.
Preheat oven to 425° F. Line a baking tray with parchment paper or Silpat baking mat.
Combine the cheeses.
Lightly toast four slices of bread.
Spread each bread slice with a layer of béchamel, spreading it all the way to the edges. Place the 4 slices of toasted bread, béchamel side up, on the prepared baking sheet.
Top each with a piece of ham, ⅛ of the cheese mixture. Place remaining untoasted slices of bread on top, béchamel side up, then top with remaining cheese.
Bake at 425º for about 5-6 minutes, until cheese is melted. Switch the oven to high broil and broil until the cheese on top is lightly golden, about 3 minutes.