Stuffed Portobello Burgers

Heat outdoor grill. Brush mushrooms and onion slices with 3 tablespoons oil. Grill onion and mushrooms, gill sides down, 12 minutes, turning after 6 minutes, or until onion and mushrooms are crisp-tender. Meanwhile brush cut sides of bread with 2 tablespoons oil. Grill, cut sides down, 2 minutes or just until lightly toasted. Transfer to a platter; cover with foil to keep warm. Mix remaining 1 tablespoon oil, the vinegar, garlic, and 1/4 teaspoon each salt and pepper. Using a spatula, place an onion slice in the cavity of each mushroom and brush with vinegar mixture. Top each with cheese, 3 basil leaves, and a tomato slice. Drizzle tomatoes with oil, if desired, and sprinkle with remaining salt and pepper. Cover grill and cook 2 to 3 minutes or until cheese is melty and soft. To serve: Place a mushroom "burger" on each piece of grilled bread. Cut a few basil leaves in thin strips and sprinkle on burgers for garnish.