1. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add mushrooms and garlic to pan; sauté 3 minutes or until mushrooms are tender. Remove from heat; set aside.
2. Combine mayonnaise, tomatoes, and capers in a mini food processor; pulse until well combined. Spread 1 tablespoon mayonnaise mixture over each of 4 bread slices; top each with 1/4 cup mushroom mixture, 2 ounces chicken, 1 cheese slice, and 1 bread slice.
3. Heat a large grill pan over medium heat. Coat pan with cooking spray. Add sandwiches to pan. Place a cast-iron or other heavy skillet on top of sandwiches; press gently to flatten sandwiches. Cook 2 minutes on each side or until bread is toasted (leave cast-iron skillet on sandwiches while they cook).