In a small bowl, combine basil, mayonnaise and vinegar; set aside.
Lightly coat both sides of mushroom caps with cooking spray; season with salt and pepper.
Grill mushrooms over medium-hot coals, about 6 minutes each side or until just soft to the touch.
To serve, split rolls and toast on grill. Spread a heaping teaspoon of basil mixture on top and bottom halves of rolls. Layer each bottom half with one red pepper, mushroom, onion slice and lettuce leaf; top with remaining half of roll and serve.