1) Beat eggs in a shallow dish (large enough to fit a sandwich) along with a few pinches of salt and pepper. Set aside.
2) Assemble sandwiches, with mustard, mayonnaise, ham, cheese, salt and pepper to personal preference. Slightly compress sandwich.
3) Heat skillet over medium heat. Add butter; allow to melt.
4) Dip and coat each sandwich in beaten egg, and place in skillet. Cook sandwiches 2-3 minutes on each side, until browned to liking and cheese has melted.
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