Pappardelle Pasta Dough
In a bowl, mix together all ingredients until combined. Transfer the dough to a lightly floured work surface and knead until smooth, about 10 minutes. Cover with plastic wrap and allow to rest for 1 hour. Divide dough into 4 equal parts and roll each through a pasta machine, starting with the thickest setting and ending with the second to last. Cut the pasta sheets into 1 1/2" wide by 6" long strips. Sprinkle with flour and refrigerate until needed.
In a large saute pan, brown the duck legs in the olive oil over medium heat, approximately 8 minutes. Remove the duck legs and keep warm on a plate tented with foil. Add to the skillet the onion, celery, carrot, and garlic and cook for 10 minutes. Deglaze the pan with wine and add the tomatoes and chicken stock. Return the duck to skillet, cover with foil, place on the middle rack of a 350 degrees oven and cook for about an hour, or until the duck is tender when poked with a fork. When the duck has cooled, remove the meat from the bones, cut into 1" pieces and add to the sauce. Season with salt and pepper.
Duck Ragu Note:
TO FINISH: Bring a sauce pan of salted water to a boil. Add the pasta and simmer until cooked, about 3 minutes. Strain the pasta and add to the sauce. Toss with parmiggiano cheese and serve.