Beat the eggs in a shallow dish ( Large enough to fit a sandwich) along with a few pinches of salt and pepper. Set aside.

Assemble sandwiches, with mustard, mayonnaise, ham, cheese, salt and pepper to personal preference. Slightly compress sandwich.

Over medium heat butter in skillet.

Dip and coat sandwich in beaten egg, and place in skillet. Cook sandwiches 2-3 minutes on each side, until browned to liking and cheese has melted.