Step 1Heat the oven to 300 degrees. Place the duck legs on a cutting board and remove the skin (discard, or save it for another use). Season each leg on both sides with a pinch of salt and pepper.
Step 2Heat a 5-quart oven-proof Dutch oven or lidded pot over medium-high heat and add 2 tablespoons oil. Sear the duck legs on both sides to golden brown, 8 to 10 minutes. Remove to a plate and set aside.
Step 3Heat the pancetta in the same pan until brown and crispy, 1 to 2 minutes, stirring constantly. Remove to a plate and set aside.
Step 4Heat the remaining tablespoon of olive oil in the pan and add the onion, cooking until caramelized, about 10 minutes. Stir in the celery and carrots and continue to cook for 10 minutes, stirring occasionally.
Step 5Add the pancetta and duck legs back to the pot. Stir in the wine and broth, adding additional broth if needed to cover the contents. Stir in the canned tomatoes and bring the mixture to a boil over high heat.
Step 6Remove from heat, cover the pot and place it in the oven. After 15 minutes, check to see that the contents of the pot are simmering gently. Re-cover and continue to cook until the meat is tender and falling off the bone, 2 to 3 hours. Check every half-hour to prevent over-cooking and to make sure there is sufficient liquid in the pot to keep the duck moist.
Step 7Remove the pot from the oven to the stove top and remove the duck legs from the pot. Separate the meat from the bones and chop the meat into large pieces. Place the meat back in the pot and discard the bones.
Step 8Heat the pot over medium heat and cook the ragu for 5 minutes, stirring frequently. Remove from heat and keep warm.
Step 9Meanwhile, bring a big pot of salted water to a boil for the pasta. Cook the pasta according to the manufacturer's instructions, about 8 to 10 minutes for al dente. Drain the pasta.
Step 10On the stove top, in another large pan, heat the butter and about 4 cups of the ragu over medium heat. Then add all of the pasta to combine. Add additional ragu to taste and continue cooking until the pasta is nicely coated and combined with the ragu, about 10 minutes. Serve in warm bowls with freshly grated Parmigiano-Reggiano cheese and chopped parsley.