Form ground beef into 2 cm thick (approximately 3/4 inch thick) rounded patties. Heat clarified butter in a heavy pan and fry hamburgers, 3-4 minutes per side. Season with salt and pepper. Rinse and pat lettuce dry. Rinse and slice tomatoes. Peel and slice onion into rings.
Halve buns. Spread bottom halves with 1 tablespoon ketchup each. Layer with lettuce and tomato slices, top with burgers and 1 tablespoon mayonnaise each. Top each sandwich with a slice of cheese and the top half of each bun. (see below for decorating instructions. Decorate before serving.)
To decorate buns: With a brush, paint 5 pentagons each bun. Sprinkle with black sesame seeds and press gently to help them adhere. Then place buns on burgers. Serve "football-style" burgers immediately.