Whisk the vinegar, garlic, onion, cumin, chipotle powder, olive oil, liquid smoke, maple syrup, lime juice, and salt and pepper together in a small bowl. Place the mushroom caps top side up on a large platter and pour half of the marinade over each one and rub in. Flip the mushrooms over and pour the remaining marinade over the bottom of the caps. Cover and let sit for at least an hour in the refrigerator.
Make the mozzarella fifteen minutes before you're ready to grill the mushrooms.
Grill the mushrooms on medium heat until they brown and soften, flip and grill until the other side begins to brown and soften. Approximately 5 to 7 minutes per side.
If you don't have a grill, heat a large skillet or grill pan on medium high heat and cook for approximately 7 to 10 minutes per side.
Place the mushroom on a bun, top with the cheese, lettuce, and tomato, and drizzle with balsamic vinegar.