Melt butter in pan. Add onions and caramelize (cook until they start to turn black). Then push onions to sides of pan (to stop cooking, but keep warm) and put ground beef patty(s) into center of same pan. When patty is brown on one side, turn and top with cheese slice. Turn heat on low and cover pan so cheese will begin to melt.
While onions and beef are cooking, arrange plate with lettuce, then tomatoes. Spread thin layer of mayonaise over all (to taste).
When meat is cooked, center ground beef patty on lettuce. Spread mustard and ketchup over top of cheese, then cover with the cooked onions. Garnish lettuce with pickles and serve.