Use tomatoes held at room temperature until fully ripe; core and cut into halves. Preheat broiler.
On shallow pan, arrange tomato and onion halves cut side down. Place garlic cloves around vegetables.
In a cup, mix oil, vinegar, sugar, salt and pepper. Brush over vegetables, coating completely. Broil 3-4 inches from heat source until lightly charred, 10-15 minutes, removing garlic cloves as they brown and soften, and turning pan around for even cooking.
Turn vegetables over and broil until lightly charred and tender, about 10-15 minutes longer. Remove pan from broiler and cool; peel skins from tomatoes.
In food processor or blender, puree tomatoes, onions and garlic with pan juices until fairly smooth. Pour into medium saucepan; stir in chicken broth.
Bring to a boil; reduce heat to medium-low. Cover and simmer to blend flavors, about 10 minutes. Remove from heat but keep warm.
To make bread bowls: preheat oven to 400 degrees. Using sharp knife, cut off top of each roll. Pull out soft centers, leaving 1/2-inch-thick shells; discard soft bread.
Reserve tops. Place bowls and tops on baking sheet. Bake until crisp, about 5-8 minutes, turning once.
To serve, place rolls in soup plates. Ladle hot soup into and around bowls. Top with cheese cubes. Garnish with basil or parsley, if desired. Serve immediately.