Prepare the béchamel sauce by melting 2 tablespoons of butter in a saucepan over medium heat. Add 2 tablespoons of all-purpose flour and whisk continuously for 2 minutes. Gradually add 250 ml of milk, whisking constantly until the sauce thickens. Season with salt, black pepper powder, and a pinch of nutmeg. Remove from heat and set aside.
Preheat a sandwich press or grill pan over medium heat.
Take 8 slices of bread and spread a thin layer of béchamel sauce on one side of each slice. Place 4 slices of bread, sauce side up, on a clean surface.
Layer 100 grams of thinly sliced ham and 100 grams of grated Gruyère cheese on top of the béchamel-covered slices. Top with the remaining slices of bread, sauce side down.
Spread a thin layer of softened butter on the outer sides of each sandwich.
Place the sandwiches in the preheated sandwich press or grill pan and cook for 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.