This is a Sunday supper sort of sauce, something you make when you have time to hang around the house. This makes a decent amount already, but you can double the recipe for either big groups or to eat all week. As for a pasta choice, really anything goes. Wide, flat pappardelle or the slightly narrower tagliatelle are traditional, but I really like this ragu with short shapes like gemelli or cavatelli. Or you could go the gnocchi route, which is what I did here.
Lay out all the duck legs and wings skin side up on a roasting pan. Sprinkle some salt over them and pop them in the oven. Turn the heat to 400°F. Don't preheat the oven, because you want the fat in the duck to slowly render out. If you happen to be using skinless legs and wings, you will need to coat them all in olive oil before you salt them. Regardless, roast until they are nicely browned, about 45 minutes to 1 hour.
Meanwhile, soak the dried mushrooms in hot water for 30 minutes, then remove and chop. Strain the mushroom water through a paper towel to remove debris and reserve.
When the duck legs have about 15 minutes to go, heat a large Dutch oven over medium-high heat and add the duck fat. When it melts, add the minced onion, celery and carrot and brown them well. Salt the veggies lightly as they cook. When the vegetables are getting brown, add the tomato paste and mix it in well. Cook the mixture until the tomato paste begins to turn brick red, about 5 minutes.
If the duck legs aren't ready, turn the heat off on the Dutch oven. If they are, remove the legs and put them in a bowl or something. If there is a lot of fat in the pan, drain it off. Pour the mushroom water and the white wine into the roasting pan and use a wooden spoon to scrape up the browned bits. Pour this into the pan with the Dutch oven. If the legs aren't ready, hang tight until they are and then do this.
Mix the liquid from the roasting pan into the tomato paste-vegetable mixture and bring to a boil. Cook it down by half. Add the duck legs and any juices that have collected in the bowl to the Dutch oven. Cover with the duck broth and the tomato puree, add the bay leaves and oregano and mix well. Bring to a gentle simmer and let this cook for at least 90 minutes. It will look like duck stew at this point, which is good. You want everything to cook down slowly.
You're ready when the meat wants to fall off the bones. Fish out all the legs and shred the meat off, then return it to the pot. If the "stew" has cooked down into a nice pasta sauce, you're good to go. If it hasn't, turn the heat up and boil it down until it's as thick as you like. Add salt and black pepper to taste when you are ready to serve. At the last minute, stir in the parsley and you're ready to rock. Grate some cheese over everything at the table.
This sauce will keep a week to 10 days in the fridge and will freeze for a year.