Grilling time: 8 to 10 minutes
Special equipment: perforated grill pan
1. Prepare the grill for direct cooking over low heat. Preheat a grill pan over direct low heat for about 10 minutes.
2. In a medium bowl combine the tomatoes, onion, garlic, thyme, and oil and toss to coat. Using tongs arrange all the vegetables and herbs on the grill pan and cook over direct low heat, with the lid closed as much as possible, until the tomato skins wrinkle and start to brown, 20 to 25 minutes, turning occasionally. Transfer the tomatoes to a large saucepan. Continue to cook the onions, garlic, and thyme until the onions and garlic are lightly charred on all sides, 5 to 10 minutes. Add the onions and garlic to the saucepan. Discard the thyme.
3. Add the chicken broth to the saucepan. Bring to a boil, reduce the heat, and simmer until the tomatoes collapse completely, 8 to 10 minutes. Transfer the soup to a blender and puree until very smooth. Pour the soup through a mesh strainer to remove all the tomato seeds and skin. Season with the sugar, salt, and pepper.
4. If the grill has an infrared burner above the warming rack, preheat the burner on high, with the grill lid open. Butter one side of each slice of bread. Top each buttered side with about 1 teaspoon of cheese. Using tongs position the bread slices on the warming rack (toward the back) just in front of the burner. Cook, with the lid open, until the cheese melts and browns, about 2 minutes. Watch carefully so the cheese doesn't burn. Remove the croutons from the warming rack. If your grill does not have an infrared burner, toast the croutons under a broiler.
5. Just before serving, reheat the soup, if necessary, and add the basil. Ladle the soup into bowls and float the croutons on top. Garnish with any remaining cheese. Serve warm.