In a large deep frying pan, heat 1 tablespoon of the oil over moderately high heat. Add the sausage and cook, breaking up the meat with a fork until no longer pink, about 3 minutes. Tilt the pan and spoon off all but 2 tablespoons fat. Reduce the heat to moderate. Add the carrots, onion, and garlic and cook, stirring occasionally, until the vegetables start to soften, about 5 minutes. Stir in the wine and let simmer 3 minutes. Add the tomatoes, broth, 4 tablespoons of the parsley, the bay leaf, and 1/2 teaspoon of the salt. Simmer, covered, for 15 minutes. Uncover, add the pepper, and simmer 5 minutes longer. Remove the bay leaf. Stir in the cream and the remaining 2 tablespoons parsley. Meanwhile, in a medium saucepan, bring the water and the remaining 1 1/4 teaspoons salt to a boil. Add the cornmeal in a slow stream, whisking constantly. Whisk in the remaining 3 tablespoons oil. Reduce the heat and simmer, stirring frequently with a wooden spoon, until the polenta is thick, about 20 minutes. Stir in the Parmesan. Serve the polenta topped with the meat sauce. Pass additional Parmesan.