Whisk flour into melted butter and cook for 1 minute. Whisk in milk and bring to a bubble then drop heat to low. Season the sauce with salt, pepper, nutmeg and dijon. When sauce coats back of a spoon, turn off heat.
Butter outsides of bread, toast ham and cheese, and then top with another slice of Gruyere.
Spoon white sauce over toasted sandwich and top with a poached egg.