Combine first 6 ingredients in a large zip-top plastic bag. Add mushroom caps; seal and marinate in refrigerator 24 hours.
Prepare grill or broiler.
Remove mushroom caps from bag, discarding marinade. Place mushroom caps on grill rack or broiler pan coated with cooking spray; cook 5 minutes or until tender.
Heat the oil in a medium nonstick skillet over medium-high heat. Add onion; cover and cook 10 minutes or until golden brown, stirring frequently.
Combine mayonnaise and roasted garlic in a small bowl. Spread 1/2 tablespoon mayonnaise mixture evenly over the top halves of buns; top each bottom half of bun with 1 lettuce leaf, 1 tomato slice, 1 mushroom cap, 1 tablespoon caramelized onion, and top half of bun.