Rinse red beans. In a large pot combine beans and 6 cups of the water. Bring to boiling; reduce heat. Simmer, uncovered, for 2 minutes. Remove from heat. Cover and let stand for 1 hour. (Or place beans and 6 cups of the water in the pot. Cover and let soak in a cool place for 6 to 8 hours or overnight.) Drain and rinse beans.
Return beans to pot; add the remaining 6 cups water and the bay leaf. Bring to boiling; reduce heat. Simmer, covered, about 1-1/2 hours or until beans are tender. Drain and rinse beans. Discard bay leaf.
In the same pot heat oil over medium heat. Add fennel, onions, carrots, celery, and garlic; cook until vegetables are tender, stirring occasionally. Stir in broth and tomatoes. Bring to boiling; reduce heat. Simmer, covered, for 30 minutes. Stir in cabbage, green beans, and red beans. Return to boiling; reduce heat. Simmer, covered, for 30 minutes more. Stir in basil.
Drop Herbed Polenta Dumplings dough into small mounds onto hot soup. Cover and simmer for 10 minutes more. (Do not lift cover during cooking.) If desired, sprinkle each serving with cheese.
Herbed Polenta Dumplings
In a large saucepan combine the 2 cups chicken broth, the Italian seasoning, and salt. Bring to boiling. In a medium bowl stir together polenta mix and the 1 cup chicken broth. Gradually add polenta mixture to broth mixture, stirring constantly. Cook and stir until mixture returns to boiling. Reduce heat to low. Cook about 5 minutes or until thick, stirring frequently (mixture may spatter). Remove from heat. Stir in Parmesan cheese and whipping cream. Using a small cookie scoop or two spoons, drop mixture into 25 to 30 mounds onto a greased baking sheet. (If mixture is too soft to form mounds, cool about 15 minutes before scooping.) Cover and chill until ready to add to soup.