Preheat oven to 400 degrees F. In a large saucepan bring water to boiling. Stir in farro; reduce heat. Simmer, covered, about 25 minutes or until tender. Drain. Set aside.
Meanwhile, line a large baking sheet with parchment paper or foil; set aside. Coat both sides of mushroom caps lightly with cooking spray. Sprinkle stem sides of mushrooms with pepper. Arrange mushrooms stem side up on the prepared baking sheet. Bake about 15 minutes or until mushrooms are just tender. Set aside.
In a large nonstick skillet heat olive oil over medium heat. Add leeks, dried tomatoes, basil, garlic, and thyme. Cook and stir for 4 to 5 minutes or until leeks are tender. Gradually stir in chard. Cook and stir for 2 to 3 minutes or until chard wilts. Remove from heat. Stir in cheese, farro, and vinegar.
Fill mushroom caps with chard mixture. Bake about 10 minutes or until heated through.