Wash the duck pieces, remove all visible fat and set aside for cicciolli. Pat dry.
In a thick-bottomed casserole or Dutch oven, heat the olive oil until almost smoking over medium-high heat. Season the duck pieces with salt and pepper and cook until brown on all sides, 10 to 12 minutes.
Remove the duck pieces to a plate and add the onion, carrot, garlic, celery, and sage to the casserole and cook over low heat until softened, 7 to 9 minutes. Add the wine, tomatoes and chicken stock and bring to a boil. Add the duck pieces, then lower the heat, cover, and simmer for 1 hour.
Remove the duck pieces, and when cool enough to handle pull all meat off the bones. Return the meat to the pot and simmer uncovered 30 minutes, or until quite thick. Season with salt and pepper and set aside.
Divide the prepared pasta dough into 3 evenly-sized balls. Roll each ball out to the thinnest setting on a pasta rolling machine. Cut the pasta into 2-inch squares, and roll each square around a dowel, corner to corner, to form quills. Place the garganelli on a sheet tray dusted with semolina, cover with a damp towel and set aside.
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12 to 14-inch saute pan, place enough ragu to coat but not overwhelm the pasta and toss over medium heat to heat through.
Drop the garganelli in the boiling water and cook 2 minutes, until tender yet al dente. Drain the pasta, reserving the water, and add the pasta to the ragu. Toss over high heat 2 minutes to coat, adding a splash of the pasta cooking water if necessary to keep the sauce at the proper consistency. Divide the pasta among 4 warmed pasta bowls, grate Parmigiano over each bowl and serve immediately.
Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and the olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.