Cook 3/4 cup minced sweet onion in 3 tablespoons butter until soft. Add 1 1/2 pounds peeled, seeded, chopped tomatoes with their juices and 1 teaspoon tomato paste. Cook 5 minutes. Add 2 cups chicken broth, a basil sprig, salt and pepper. Cook 15 minutes, discard basil and puree soup.
Panera Bread's recipe recommends cooking 1 large chopped onion, 1 minced garlic clove and 2 ribs chopped celery in 1 tablespoon each of olive oil and butter over medium heat. When vegetables are soft but not browned, stir in 1 tablespoon flour and cook for one minute. Add 4 pounds coarsely chopped super-ripe tomatoes with their juices, 4 fresh basil leaves, 1 teaspoon sugar, 3/4 teaspoon salt, and 1/2 teaspoon freshly ground black pepper. Bring the tomatoes to a boil over high heat, then reduce heat to medium and simmer for 15 minutes, skimming off foam. Puree soup in a blender, run through a food mill or strainer to remove any solids, and return processed soup to pot to heat through. Divide soup between four bowls and garnish each with freshly chopped basil.
For variation, cook 1 cup chopped onion in 1 tablespoon olive oil until tender. Stir in 5 medium-sized peeled and chopped ripe tomatoes, their juices, 1 1/2 cups vegetable broth, 1 6-ounce can tomato paste, 1 teaspoon salt, 1/4 teaspoon ground nutmeg and 1/8 teaspoon cayenne pepper. Simmer uncovered until tomatoes are soft, then add 1/2 cup whipping cream. Puree in a blender or food processor, reheat and garnish with chopped basil.