Split the buns and toast.
In a small pan, melt the butter.
Add the flour to the butter, stirring to remove lumps. Cook for about three minutes.
Pour in the milk in a slow steady stream, stirring as you pour. Cook, stirring, until the mixture is thick.
Stir in the mustard and ham.
Off the heat, stir in the mozzarella and cheddar. Mix until melted. Taste. Add just enough salt and pepper to flavor the mixture.
Spread about two heaping tablespoons of the ham and cheese mixture on each toasted half bun.
Grill in the broiler (or in the oven with only the top heat on) at 400F for about five minutes or until the cheese and ham topping is melted and lightly browned.