Preheat the oven to 200°C/390°F (180°C fan).
Warm the milk and cream in a saucepan over medium heat until steaming, then set aside.
Melt butter in a small saucepan, stir in flour, and cook on low for 3 minutes without letting it brown.
Slowly whisk in the hot milk mixture, add nutmeg, salt, and pepper, and cook until the sauce is thick and spreadable. Remove from heat.
Spread half the béchamel over the bread slices, then layer cheese, Dijon mustard, smoked turkey, and more cheese before closing the sandwiches.
Melt butter in a skillet, pan-fry the sandwiches on both sides until golden, then move them onto a baking tray.
Spread the remaining béchamel on top, sprinkle Gruyere and Parmesan, bake for 15 minutes, then broil for 3 minutes until bubbling and golden.
Serve hot with fries or a simple green salad.