For the duck: Preheat the oven to 325 degrees F. Sear the duck legs over medium heat in a large skillet until the fat is rendered out and the skin is crisp, then remove and let rest on a rack. Add the onions, carrots, celery, leeks and garlic to the fat in the skillet and cook until the onions are translucent. Stir in the tomato paste and cook for a few more minutes, and then add the wine and bring up to a simmer. Add the stock and tomatoes and return to a simmer. Return the duck to the skillet, cover and transfer to the oven for 2 hours 30 minutes to 3 hours.
For the pasta: Mix together the flour and salt in a mound on the table, and then make a well in the center. Whisk together the oil, eggs and egg yolks, and pour into the well. Gently stir in the wet ingredients until combined, and then knead the dough into a ball. Wrap in plastic and refrigerate for 1 hour, and then roll out to desired thickness and cut into wide papardelle.
Remove the duck from the liquid and let cool at room temperature. Strain the cooking liquid. Bring a pot of salted water to a boil. Pull the duck meat from the bones and shred into bite-size pieces.
Boil the pasta for 4 minutes, then drain. Meanwhile, heat the canola oil in a large pan, and then saute the mushrooms and chard until tender. Add 4 ounces of the braising liquid and the braised duck, followed by the pasta, tossing to coat. Remove from the heat and swirl in the butter to melt. Season with salt and pepper.
NotesThis recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens have not tested it for home use and therefore cannot make any representation as to the results.