Step 1

Arrange a rack in the upper third of the oven and heat the oven to 425ºF.

Step 2

Melt 2 tablespoons unsalted butter in a small saucepan over medium heat. Add 2 tablespoons all-purpose flour and whisk until combined, about 1 minute. While whisking constantly, slowly pour in 3/4 cup whole or 2% milk. Bring to a simmer (it will start to thicken up), whisking constantly.

Step 3

Remove the saucepan from the heat. Add 2 teaspoons Dijon mustard, 1/8 teaspoon ground nutmeg, 1/8 teaspoon kosher salt, and 1/8 teaspoon black pepper, and whisk to combine.

Step 4

Line a baking sheet with parchment paper. Grate 6 ounces Gruyère cheese on the large holes of a box grater(about 2 cups). Place 4 (1/2-inch) thick slices bread on the baking sheet. Spread 2 tablespoons béchamel on each slice of bread. Divide 6 to 8 ounces sliced ham over the béchamel, bending and folding then as needed to fit. Sprinkle half the cheese on top of the ham.

Step 5

Close the sandwiches with the remaining 4 bread slices. Spread 2 tablespoons béchamel evenly onto each slice of bread. Sprinkle with the remaining cheese.

Step 6

Bake until the edges of the bread are crispy and the tops are starting to brown, about 15 minutes. Heat the oven to broil. Broil until deep golden brown in spots, about 3 minutes more. Let cool for 5 minutes before serving.