1. Combine carrot, onions and garlic in a 6-quart slow cooker.
2. Rinse ribs and pat dry; season with salt and pepper. Heat oil in a large, wide pot over moderately high heat until hot but not smoking. Add ribs, in batches, and cook, turning, until browned on all sides, about 15 minutes. Transfer, as cooked, to slow cooker.
3. Stir together tomatoes, broth, wine, parsley, cornstarch and tomato paste in a bowl; pour over ribs. Add bay leaf. Cover and cook, 9 to 11 hours on low or 4-1/2 to 5-1/2 hours on high. Skim off any fat from top (discard bay leaf).
4. Combine 3-3/4 cups water, the polenta and salt in a large saucepan over moderately high heat. Bring to a boil, stirring constantly. Add cheese and cook, stirring constantly, until thickened, about 5 minutes.
5. Serve ribs over polenta and garnish with parsley, if desired.