Heat closed contact grill 5 minutes. In medium bowl, mix mushrooms, onion, 1 tablespoon of the Worcestershire sauce and 1/4 teaspoon of the garlic-pepper blend.
When grill is heated, place mushroom mixture on bottom grill surface. Close grill; cook 3 to 4 minutes or until mushrooms are tender. Remove from grill; cover to keep warm.
Brush both sides of beef patties with remaining tablespoon Worcestershire sauce; sprinkle with remaining 1/4 teaspoon garlic-pepper blend. Place patties on bottom grill surface. Close grill; cook 4 to 6 minutes or until thoroughly cooked. Top each patty with cheese slice (do not close grill); cook until melted.
Spread bottom halves of buns with mustard-mayonnaise sauce. Top each with mushroom mixture, cheese-topped beef patty and top half of bun.