Heat your oven to 400ºF and arrange the rack in the middle of the oven.
Melt butter in a medium pan or saucepot over medium heat. Sprinkle over the flour and whisk to combine. Cook, whisking constantly, for 30 seconds to toast the flour. While whisking, slowly pour in the warmed milk and season the mixture with salt, pepper, Herbes de Provence, and a pinch of nutmeg. Bring to a simmer and turn the heat down to medium-low, stirring occasionally, until the mixture is thick, creamy, and will coat the back of a spoon.
Once thick, whisk in the Parmigiano Reggiano and ½ cup of Gruyere and keep warm over low heat.
Meanwhile, very lightly toast the bread and lay it out on a baking sheet. Spread the Dijon mustard over half the slices and top with ham, if using. Spread about 3 to 4 tablespoons of the béchamel on top and sprinkle each with ¼ cup of grated Gruyere cheese. Top each with a remaining slice of bread and divide over the remaining béchamel and Gruyere.
Transfer the sandwiches into the oven for 5 minutes to melt the cheese and heat through. Turn on the broiler on to high and broil for 2 to 3 minutes or until the tops are golden and bubbling.
