Wash and drain the lettuce and tomatoes. Cut the tomatoes into slices. Peel onions, finely dice one onion and cut the other into thin rings. Drain cucumber slices.
Knead minced meat, diced onion and egg, season with salt and pepper. Form 4 flat minced steaks. Heat oil in a pan and fry the steaks on each side for about 2 minutes. In the meantime cut the rolls and cover the lower halves with lettuce, cucumber, tomatoes and onion.
Spread ketchup and mayonnaise over it. Put cheese slices on the hot minced steaks and place them on the rolls. Cover with the top halves of the rolls and serve immediately.