PreparationFor soup: Prepare barbecue (medium-high heat). Lightly oil grill rack. Cut 1-inch-wide slice from top and bottom of bell pepper and reserve. Cut pepper open lengthwise and press flat. Cut off ribs and remove seeds; discard. Grill tomatoes, flattened pepper, and top and bottom slices of pepper until skins are charred, turning occasionally, about 7 minutes for tomatoes and 10 minutes for pepper; transfer to plate to cool. Peel tomatoes and pepper; coarsely chop pepper. Puree tomatoes, pepper, 1/2 cup tomato-vegetable juice, and next 3 ingredients in processor until almost smooth. Transfer to bowl. Add 1 1/2 cups tomato-vegetable juice; season soup to taste with salt and pepper. For pesto: Finely chop basil leaves, pine nuts, and garlic in processor. With machine running, add oil and puree until almost smooth. Season pesto to taste with salt and pepper. (Soup and pesto can be made 1 day ahead. Cover separately and refrigerate.) Divide soup among 6 bowls. Top each with 1 spoonful pesto; serve with breadsticks.
PreparationFor soup: Prepare barbecue (medium-high heat). Lightly oil grill rack. Cut 1-inch-wide slice from top and bottom of bell pepper and reserve. Cut pepper open lengthwise and press flat. Cut off ribs and remove seeds; discard. Grill tomatoes, flattened pepper, and top and bottom slices of pepper until skins are charred, turning occasionally, about 7 minutes for tomatoes and 10 minutes for pepper; transfer to plate to cool. Peel tomatoes and pepper; coarsely chop pepper. Puree tomatoes, pepper, 1/2 cup tomato-vegetable juice, and next 3 ingredients in processor until almost smooth. Transfer to bowl. Add 1 1/2 cups tomato-vegetable juice; season soup to taste with salt and pepper. For pesto: Finely chop basil leaves, pine nuts, and garlic in processor. With machine running, add oil and puree until almost smooth. Season pesto to taste with salt and pepper. (Soup and pesto can be made 1 day ahead. Cover separately and refrigerate.) Divide soup among 6 bowls. Top each with 1 spoonful pesto; serve with breadsticks.