Soak the porcini mushrooms in boiling water for at least 20 minutes. Strain and reserve the mushrooms and liquid separately. Finely chop the mushrooms and put aside. Strain the tomatoes and reserve the juice for another use. Chop the tomatoes into approximately 1/2" pieces and reserve.
Heat the olive oil in a large pot over medium-low heat. Add the onions, carrots and celery and cook gently for 10 minutes or until vegetables are very soft and just beginning to brown. Stir in the garlic and parsley and cook for another 3 minutes.
Add the beef, pork and veal and saute until the meat loses its pinkness, about 5 - 7 minutes. Add the reserved mushrooms and season with salt and pepper. Add the red wine and boil until the wine is mostly evaporated and the mixture is saucy. You don't want it dry, just a little saucy. Stir in the beef stock, mushroom soaking water, tomato paste and tomatoes.
Bring to a boil and reduce the heat to low and cover. Simmer for about 1 hour. Re-season and add the whipping cream and nutmeg. Simmer, covered for 10 minutes longer or until the flavors are combined.
While the sauce is cooking add the pasta to a large pot of boiling salted water and boil until the pasta is just al dente. Drain well.
Toss the pasta with the sauce and sprinkle with Parmesan.
Serve with a little more freshly grated Parmesan.