Heat heavy large cast iron or non-stick skillet or griddle on medium heat. Meanwhile, combine ground beef, Worcestershire sauce, pepper, and salt in medium bowl, mixing lightly but thoroughly. Lightly shape into four 1/2-inch thick patties. Place patties in skillet; cook 10–12 minutes until instant-read thermometer inserted horizontally into center of patty registers 160 degrees for medium doneness, turning occasionally. Remove from skillet; keep warm. Melt 1 tablespoon butter in same skillet. Add onion; cook 6–8 minutes or until golden brown and very tender, stirring often. Remove onions from skillet; keep warm. Spread remaining 1 tablespoon butter on one side of each bread slice half. Place 2 bread halves, buttered-side down in skillet. Layer each with 1 slice American cheese, 1 burger, and 1 slice Swiss cheese, quarter of onion mixture, top with bread, buttered-side up. Weight down sandwiches with heavy pan; cook 1–3 minutes on each side or until bread is golden brown, turning sandwiches once. Repeat with remaining bread, burgers, and cheeses.