Bechamel: MELT butter in a medium saucepan over medium heat. Whisk in flour and cook, stirring constantly, for about 3 minutes. Gradually add milk, stirring until the mixture is smooth. Cook and stir until sauce is thickened.
Sandwich Assembly: PREHEAT oven to 425° F. Line a baking sheet with parchement paper and set aside.
LAY your donut halves out - half glazed side up, half unglazed side up.
SPREAD each donut half with a layer of béchame all the way to the edges. Place the 4 unglazed-side up donut halves on the parchment lined baking sheet, béchamel side up.
TOP your unglazed side up halves with a slice of Pan Roasted Turkey, a slice of Virginia Ham, a handful of provolone, and a sprinkle of parmesan cheese. Place remaining donut halves 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, 2-3 minutes.