In a small bowl, stir together tomato, desired herb, and salt; set aside. Cut the mushroom stems even with the caps; discard stems. Rinse mushroom caps; gently pat dry.
In a small bowl, stir together vinegar and oil. Gently brush vinegar-oil mixture over the mushrooms. Grill mushrooms on the rack of an uncovered grill directly over medium coals for 6 to 8 minutes or just until tender, turning once. Thinly slice mushrooms.
Place bread on the grill rack during the last 2 to 3 minutes of grilling to heat through.
To serve, top bread with mushrooms and tomato mixture. If desired, sprinkle with Parmesan cheese. Makes 4 servings.