In a large pot, heat the fat back over medium heat. Add the carrot, onion, celery, garlic, parsley, and bay leaf and cook over medium heat until the garlic begins to brown. Add the bone and enough water to cover it, season with plenty of salt and pepper, and bring to a boil. Add the beans and cook for 1 hour, then add the pasta, cooking at a boil until the pasta is tender yet al dente. Serve immediately, divided evenly among 4 warmed pasta bowls.