Prepare grill.
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, juice, and soy sauce in a small bowl; brush over both sides of mushroom caps.
Place the mushroom caps, stem sides down, on grill rack coated with cooking spray, and grill for 5 minutes on each side or until soft.
Grill the mushrooms stem sides down first, so that when they’re turned they’ll be in the right position to be filled.
Spoon 1/4 cup tomato mixture into each mushroom cap.
Cover and grill 3 minutes or until cheese is melted.
Sprinkle with parsley.