1Make a charcoal fire in a pit to a medium-hot fire or heat a stovetop grill pan over medium heat. Combine olive oil, garlic , salt, and pepper; lightly brush mixture over mushrooms.
Stir pesto, mayonnaise, and lemon juice in a bowl until smooth.
Grill mushroom caps about 3 minutes per side, until tender, placing two slices of cheese on top of each mushroom during the last minute of grilling.
Spread cut sides of muffins with pesto mixture. Line muffin bottoms with lettuce leaves. Place mushrooms over lettuce, then top with roasted peppers and muffin tops.