Combine the tomato, cheese, 1/2 teaspoon oil, rosemary, pepper, and garlic in a small bowl.
Remove brown gills from the undersides of mushroom caps using a spoon, and discard gills. Remove stems; discard. Combine 1/2 teaspoon oil, lemon juice, and soy sauce in a small bowl; brush over both sides of mushroom caps. Place the mushroom caps, stem sides down, on a grill rack coated with cooking spray, and grill for 5 minutes on each side or until soft.
Spoon 1/4 cup tomato mixture into each mushroom cap. Cover and grill for 3 minutes or until the cheese is melted. Sprinkle with parsley.