Once the polenta is added to this soup, it should be the consistency of oatmeal--perfect for warming body and soul on cold winter days. Leftovers will continue to thicken and may be thinned with additional water or broth. Slices of toasted crusty Italian bread usually accompany this soup.
Heat oil in a Dutch oven over medium heat. Add cabbage, onion, and garlic; cook 12 minutes or until almost tender. Add broth, salt, pepper, and bay leaf; bring to a boil. Reduce heat, and simmer, uncovered, 12 minutes or until cabbage is tender. Slowly add polenta, stirring constantly with a whisk. Simmer 5 minutes or until thick. Discard bay leaf. Ladle soup into individual bowls, and sprinkle with cheese.