Prepare the Filling:
Place 1 tablespoon of the oil in a large skillet over medium-high heat. When the oil is hot, add the veal, season with ¼ teaspoon of the salt and ¼ teaspoon of the pepper, and cook, stirring to break up the veal, until it is well browned, about 10 minutes. Drain the veal in a colander, and discard the fat. (If using leftover braised veal, skip this step).
Add 2 tablespoons of the olive oil to the skillet. Reduce the heat to medium and add the carrots, celery root, onion, and garlic. Season with the remaining ¼ teaspoon of salt and ¼ teaspoon of pepper, and cook, stirring occasionally, until the vegetables are tender, about 15 minutes. Return the veal to the pan. Add the allspice, nutmeg, and port. Simmer for about 2 minutes, until the pan is almost dry, about 12 minutes. Add the crème fraîche and cook, stirring, for 1 to 2 minutes. Remove the pan from the heat. Add the pecorino, and season to taste with salt and pepper. Transfer the veal mixture to a bowl and reserve.
Wipe out the skillet, place it over medium-high heat, and add the remaining 2 tablespoons of oil. Add the arugula, a handful at a time, and cook, stirring, until it wilts, about 4 minutes. Season the arugula to taste with salt and pepper, then drain thoroughly. Stir the arugula into the veal mixture, cover the bowl, and refrigerate until ready to use.
Prepare the pasta (if using dough):
Divide the pasta dough into 4 small balls. Using a pasta machine, roll the dough out through successively smaller setting until it is less than 1/8 inch thick and almost translucent; this should be at about the fifth setting. (The dough tends to become fragile and rip if rolled any thinner.) Cut the dough into a total of 16 rectangles, about 4x5 inches each.
Bring a large pot of salted water to a boil over high heat. Brush a thin coating of olive oil onto a large piece of parchment paper. Prepare a bath of ice water. Cook the rectangles of pasta, a few at a time, until they float, about 45 seconds. Transfer the pasta briefly to the ice-water bath to cool, then drain. Place the pasta rectangles on the oiled parchment paper, cover them with a damp cloth, and reserve at room temperature until ready to use. (Alternatively, the cooked pasta dough can be stored in layers of oiled parchment paper stacked on top of one another.)
If using 6-inch egg roll wrappers, trim to 4x5-inch rectangles; otherwise, adjust the size and number of cannelloni according to size of wrappers.
Form the Cannelloni:
Preheat the oven to 350°F. Arrange a heaping tablespoon of veal-arugula filling along the shorter side of each rectangle of pasta dough. Roll the pasta around the filling as if you’re rolling a cigar. Repeat the process until you have formed cannelloni with all the pasta rectangles.
Place the cannelloni in one layer in an ovenproof baking dish. Distribute the sliced butter evenly over the cannelloni, sprinkle with the Parmesan, then add the stock. Place the cannelloni in the oven to bake until the cheese is melted and beginning to brown, about 15 minutes.
Sauté the Chanterelles:
Combine the oil and butter in a large sauté pan over medium-high heat. When the butter begins to foam, add the chanterelles and lightly sauté them until softened, about 5 minutes. Season with salt and pepper to taste and add the parsley.
Spoon the based cannelloni onto warm places. Top each portion with chanterelle sauce, and serve.