Preparation
Trim the excess flap of skin on each duck leg and remove visible fat. Season all over with salt and pepper. Heat the olive oil in a large pot over high heat. Add the duck, skin side down. Brown on all sides, about 5 minutes. Pour off all but 2 tablespoons fat. Add the pancetta and cook over medium heat until it renders some of its fat and begins to crisp, then add the onions, celery and carrot. Sauté until the vegetables are softened, about 10 minutes. Add the garlic and parsley and cook for a minute. Stir in the tomato paste and cook for another minute. Add the tomatoes and wine. Bring to a simmer and reduce until slightly thickened, about 5 minutes. Return the duck to the pot, skin side up. Add the stock and the sage springs and bring to a simmer. Cover and adjust the heat to maintain a gentle simmer. Simmer until the meat is tender and pulls readily from the bone, about 1-1/2 hours. Lift the duck legs out of the sauce and set them aside to cool. Skim any fat that has been released by the duck legs with a small ladle. Reduce the sauce to thicken. Add the milk and cook for minute to reduce and round out the flavors. Taste and adjust the seasoning.
Tear each kale leaf into 3 to 4 pieces. Bring a large pot of salted water to a boil over high heat. Add the kale and blanch for 30 seconds, then drain in a sieve and cool quickly under cold running water. Squeeze well to remove excess water. Chop fine.
Pull the duck meat off the bones and dice it. Return it to the sauce and reheat gently. Stir in the kale. Simmer gently for about 5 minutes to blend the flavors.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until al dente. Set aside 1 cup of the pasta water, then drain the pasta and add it to the sauce. Toss well, moistening if necessary with some of the reserved pasta water, the grated cheese and butter. Divide among warm bowls and serve immediately. Pass additional Parmesan cheese, if desired.
