First, make the béchamel sauce. Combine the Butter (2 tablespoon) and All-Purpose Flour (2 tablespoon) in a medium sauce pan and heat them up over medium high heat. Whisk them together well until it is a golden paste.
Slowly pour in the Heavy Cream (3/4 cup) until it is a uniform sauce. Then whisk in the Dijon Mustard (1 tablespoon), Salt (1 pinch) and Garlic Powder (1 pinch).
Let the mixture cook together while you whisk constantly for 3-4 minutes until it is thick and luscious. Set it aside, then preheat the oven to 425 degrees F (220 degrees C). Get out a sheet pan and line it with foil.
Lay out the Brioche (4 slice) on the sheet pan and spread 1/4 of the béchamel sauce onto each slice. Nestle two slices of Smoked Deli Ham (4 slice) into the béchamel sauce on two of the slices. Then take half of the Smoked Gouda (3/4 cup) and evenly divide it on top of the ham. Place the other two slices of bread on top with the béchamel side up and evenly divide the remaining cheese on top of that.
Finally, sprinkle a pinch of Herbes de Provence (2 pinch) on top of each sandwich. Bake them for 10-15 minutes until golden and bubbly. Serve immediately and enjoy!