Peel onions and finely chop. Heat 2 tablespoons of oil in a small frying pan and saute onion until soft. Mix ground beef with salt, pepper and cooked onions. Knead well and then shape into 4 round patties, each about 2 cm (approximately 1 inch) thick.
Heat 3-4 tablespoons of oil in a large frying pan and cook patties for about 4 minutes on each side.
Rinse lettuce and pat dry. Rinse tomatoes and cut into thin slices. Peel white onion and cut into thin rings. Cut hamburger buns and top bottom buns with lettuce leaves, hot hamburger patties, cheese, tomato slices and onion rings. Add 1 tablespoon of ketchup to each cheeseburger if desired. Place top bun on top and serve with chips and pickles if desired.