Procedure
1. Heat the olive oil up over medium-high heat in a medium sauce pan. Add the sausage, and cook until brown, about 5 minutes. Remove the sausage and reserve.
2. Add the carrots and onion to the pan, and cook, stirring often, until softened, about 10 minutes. Add the lentils, and 1 1/2 cups water. Bring to a boil and then reduce to a simmer. Simmer on low with the lid on for 15 to 20 minutes, until the water is absorbed and the lentils are tender.
3. Return the reserved sausage and add the tomato sauce, vinegar, and salt and pepper, and simmer for another 10 minutes. Serve over soft polenta, pasta, or alone, topped with a generous amount of Parmesan cheese.