Preheat grill to medium-high. Make drainage holes in a sheet of Reynolds Wrap(R) Non-Stick Aluminum Foil with a large fork; set aside.
Combine butter and garlic. Baste mushroom caps with mixture. Place foil on grill grate with non-stick (dull) side facing up. Immediately place mushrooms on foil.
Grill uncovered 6 to 8 minutes, turning once, until mushrooms are browned and tender. Place 1 slice of cheese on each mushroom during the last minute of grilling.
Combine sour cream, vinegar, mustard, sugar and pepper in small microwave-safe bowl to make sauce. Microwave on HIGH power 30 seconds or until warm. Serve sauce over burgers in buns. Add lettuce and tomato, if desired.