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 to 12 minutes until instant-read thermometer inserted horizontally into center of patty registers 160°F for medium doneness, turning occasionally. Remove from skillet; keep warm.
Melt 1 tablespoon butter in same skillet. Add onion; cook 6 to 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 slices, buttered-side up. Weight down sandwiches with heavy pan; cook 1 to 3 minutes on each side or until bread is golden brown, turning sandwiches once. Repeat with remaining bread, burgers and cheeses.
Nutrition information per serving: 455 Calories; 234 kcal Calories from fat; 26 g Total Fat; 14 g Saturated Fat; 0.5 g Trans Fat; 8 g Monounsaturated Fat; 128 mg Cholesterol; 928 mg Sodium; 22 g Total Carbohydrate; 2.6 g Dietary Fiber; 34 g Protein; 3.8 mg Iron; 479 mg Potassium; 6.3 mg Niacin; 0.4 mg Vitamin B6; 2.6 mcg Vitamin B12; 6.6 mg Zinc; 34.1 mcg Selenium; 90.9 mg Choline;