First make the stuffing. In a deep skillet cook the onion, celery and carrot in the olive oil over moderate heat, stirring occasionally, for 3 minutes, or until softened. Add the garlic and cook the mixture, stirring, 1 minute. Add the veal, pork and beef and cook, stirring occasionally, until no longer pink. Add the wine, reduce for 1 minute and stir in the broth. Add the herbs, bay leaf and salt and pepper. Bring the mixture to a boil and simmer, covered, 15 minutes. Uncover and reduce until almost dry. Discard bay leaf. Transfer mixture to a bowl and let cool. Mix in egg yolks until well combined. Meanwhile, in a saucepan set over moderately low heat melt the butter, add the flour and whisk the mixture for 2 minutes. Add the milk, nutmeg and salt and pepper and simmer the mixture, stirring occasionally, for 5 minutes, or until thickened. Stir in 1/2 cup of the Parmesan and the parsley. In a bowl combine the meat mixture with the cheese and parsley sauce. Make the tomato sauce and stir in the heavy cream.
Now, make the pasta. Cut the dough crosswise into 5-inch lengths. In a pot of boiling salted water cook the noodles, a few at a time, for 1 to 1 1/2 minutes, or until they are al dente, transferring them as they are cooked to a bowl of cold water. Spread the noodles in one layer on paper towels to drain. Spoon 1/4 cup of the filling down the center of one noodle, roll the noodle to enclose the filing, and transfer the cannelloni, seam side down, to a well-buttered gratin dish.Continue to make cannelloni with the remaining noodles and filling in the same manner, arranging them in one layer. Ladle the sauce over the cannelloni and sprinkle with the remaining Parmesan. Bake at 400 degrees F for 10 minutes or until bubbling. Run under the broiler about 4 inches from the heat, for 2 minutes, or until golden.