Preheat broiler. Form ground beef into 2-inch round, very flat patties, and place in broiler-proof pan.
Broil 3 minutes; turn patties over and broil second sides until beef is cooked to at least 155 degrees or above. Top patties with cheese. Broil patties until cheese melts.
Place each burger onto a Melba snack and top with another Melba snack. Serve with your favorite condiments.