Melt The Butter In A Heavy Saucepan Over Medium Heat. Mix In The Cheese Once It Is Melted. Dip Each Slice Of Bread Into The Melted Cheese, Coating Both Sides. Heat A Skillet Over Medium Heat. Place One Slice Of Bread Into The Skillet And Top With 2 Slices Of Ham. Place The Second Piece Of Bread On Top. Fry Until Golden On Each Side, Then Remove From The Skillet And Set Aside. Fry The Egg In The Hot Skillet To Your Liking: Easy, Medium, Or Well Done. Place The Fried Egg On Top Of The Sandwich And Serve.