1In large glass or plastic bowl or resealable food-storage plastic bag, mix oil, vinegar, oregano, thyme, salt and garlic. Add mushrooms; turn to coat. Cover dish or seal bag; refrigerate 1 hour.
2Heat coals or gas grill for direct heat. Remove mushrooms from marinade (mushrooms will absorb most of the marinade). Cover and grill mushrooms over medium heat 8 to 10 minutes or until tender. Sprinkle with cheese.