Mix minced meat with egg, mustard and breadcrumbs. Season with salt and pepper. Knead and shape into 4 patties. Cook in hot oil for 2-3 minutes on each side.
Rinse tomatoes and cut into slices.
Peel onion, cut in half, cut into strips and fry until golden brown in hot butter.
Cut rolls in half and top each bottom half with lettuce, a hamburger patty, a slice of tomato, a pepperoncini and onions. Add a slice of cheese to each hamburger and place under a preheated broiler and broil, watching carefully, for about 4 minutes or until cheese melts. Add top halves of rolls and serve.