Preheat oven to 350°F.
Add 8 oz. Gruyère cheese, 8 oz. Parmesan cheese, white pepper, and nutmeg to prepared gravy and stir to incorporate. Place on a steam table during service.
Toast English muffins until lightly browned.
Brush each muffin half lightly with Dijon mustard.
Top each muffin bottom with a 2-oz. slice of Virginia ham.
Place ½ oz. Gruyère cheese over ham and top with muffin top.
Ladle 1 oz. of cheese sauce over the top of the sandwich.
Sprinkle ½ oz. of Parmesan cheese over the cheese sauce.
Bake for 5 minutes. Broil for 2 – 5 minutes, until cheese is lightly browned.