Make bechamel sauce by melt the 2 tablespoons butter in a saucepan over medium heat. Whisk in flour and milk. Add nutmeg and bay leaf. Whisk constantly until it thickens. Once thick, season with salt and pepper. Set aside.
In a frying pan, melt 2 tablespoons butter. Fry both sides of sandwiches until golden brown.
Put fried sandwiches on a lined baking sheet. Spoon bechamel sauce over it. Add grated mozzarella and parmesan cheese.
Broil sandwiches by toasting it in a toaster or in an oven’s top rack until sauce is bubbling and golden (3 to 5 minutes).