Place a griddle or large skillet over medium heat.
Place a small pot over medium heat with the butter. Sprinkle the flour over the melted butter and cook about 1 minute. Whisk in milk and bring up to a bubble. Simmer until thickened, about 2 minutes. Remove pot from the heat and stir in some salt, pepper, nutmeg and the Dijon.
Butter one side of each slice of bread. Build the sandwiches by smearing the dry side of each slice with some of the milk sauce then stacking the ham and cheese onto four slices of bread. Cap the sandwiches off with the remaining four slices of bread, buttered side out. Cook sandwiches until golden brown and toasted, and the cheese has melted. 3-4 minutes per side. Serve warm.