1. In a small bowl, mix the mayonnaise and the ketchup. Remove the crusts from the sandwich bread. Spread the slices of ham out on your kitchen counter or a cutting board.
2. Place a slice of the crustless sandwich bread on one side. Spread it with the mayonnaise-ketchup mixture. Place the cheese on top.
3. Fold the ham over, covering the cheese. Roll up tightly and securely. If you like, place them in the fridge to firm up the ingredients. Cut into small rolls and serve.