Peel and finely chop the onion. Finely dice the ham. Knead minced meat, onion, ham, egg, breadcrumbs, cream, just under 1⁄2 tsp salt and 1⁄4 tsp pepper. Form 4 flat meatballs from the minced meat mixture with moistened hands.
Wash the tomatoes and cut into thick slices. Wash the cucumber and cut into thin slices. Wash lettuce leaves and carefully dab dry. Mix mayonnaise and ketchup.
Heat the oil in a pan. Fry the meatballs for about 5 minutes on each side.
In the meantime cut open the rolls. Spread a thin layer of ketchup mayonnaise on the cut surfaces. Cover the undersides with lettuce, meatballs, cheese, tomatoes and cucumbers, spreading the remaining ketchup mayonnaise in between.
Place the upper roll halves on top.