In a large pot, heat the oil over medium-high heat. Add the bacon and cook, stirring, until browned and the fat is rendered, 4 to 5 minutes. Add the onions, carrots and celery and cook, stirring, until soft, 10 to 12 minutes. Add the garlic, salt, pepper, bay leaves, thyme, oregano, basil, and rosemary and cook, for 3 minutes. Add the beef, veal and pork, and cook, stirring, until no longer pink, about 5 minutes. Add the tomato paste and cook, stirring, for 1 to 2 minutes. Add the Vermouth and cook, stirring, to deglaze the pan and remove any browned bits sticking to the bottom of the pan, and until half of the liquid is evaporated, about 4 minutes.

Add the diced tomatoes and their juices, crushed tomatoes, and beef broth and bring to a boil. Reduce the heat to medium-low and simmer, stirring occasionally, to keep the sauce from sticking to the bottom of the pan, until the sauce is thickened and flavorful, about 1 1/2 hours. Add the cream, butter, and parsley, stir well, and simmer for 5 minutes. Discard the bay leaves and adjust the seasoning, to taste. Remove from the heat and cover to keep warm until ready to serve.

Meanwhile, bring a large pot of salted water to a boil. Add the pasta and return the water to a low boil. Cook, stirring occasionally to prevent the noodles from sticking, until al dente, 8 to 10 minutes. Drain in a colander.

Add the pasta to the sauce, tossing to coat. Add 1/2 cup of the cheese and toss to blend. Divide among pasta bowls and serve with the remaining cheese passed tableside.

(Alternatively, toss only the desired portion of pasta with a bit of the sauce at a time in a serving bowl, reserving the remainder for another meal.)