In 8-inch skillet, cook garlic in butter over low heat 2 to 3 minutes, stirring occasionally, until garlic is tender. Stir in Worcestershire sauce. Remove from heat.
Heat gas or charcoal grill. In large bowl, mix beef and grill seasoning. Shape mixture into 8 oval patties, 1/2 inch thick.
Place patties on grill over medium heat. Cover grill; cook 10 to 12 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Remove from grill to platter; top with cheese. Place bread on grill. Cover; cook 2 to 4 minutes, turning once, until lightly toasted.
Spread one side of each toasted bread slice with butter mixture. Top bread slices with salad greens and burgers.