For The Béchamel sauce:

1. Warm the milk on low heat until little bubbles form at the edges; remove from heat.
2. Melt 2 Tbsp. unsalted butter in a heavy-bottomed saucepan over medium heat. Stir in 2 Tbsp. all-purpose flour and cook, stirring constantly, until the paste cooks and bubbles a bit, but don’t let it brown, about 2 minutes. Slowly add 1¼ cups whole milk, heated, whisking to incorporate. Bring it to a boil, stirring constantly, as sauce thickens. Add kosher salt and freshly ground black pepper to taste. Reduce to low heat, and cook, stirring, 2–3 minutes more. Remove from the heat.

To build the Sandwiches:

1. Preheat oven to 425° F. Line a baking tray with parchement paper and set aside.
2. Spread dijon mustard on first (optional) then carefully spread one side of each bread slice with a layer of béchamel, ensuring it is spread to the edges. Place 4 slices of bread, béchamel side up, on prepared baking sheet.
3. Add a slice of ham, a slice or handfull of gruyere cheese and a sprinkle of parmesan cheese onto the 4 slices of bread. Place remaining slices of bread on top, béchamel side up, then add remaining gruyere and parmesan cheese to the top.
4. Bake at 425 degrees F for about 5 minutes, until cheese is melted, then broil until the cheese on top is lightly golden, 3 minutes.