Heat the oven to 450°F. Wash and pat dry the duck. Season the duck inside and outside with salt and pepper. Place 2 bay leaves, 2 sprigs thyme, 2 sprigs rosemary, and sage in the cavity of the duck. Tie up the legs, and place duck in a roasting pan. Prick the duck all over (top and bottom) with a fork, and then roast in the oven, turning every 30 minutes, until the meat is cooked through, about 1-1/2 hours. Remove from the oven and let cool. Shred the meat from the carcass, cutting it into small pieces and discarding the skin.
Meanwhile, in a heavy casserole pan, heat the olive oil over medium heat. Add the onion, celery, and carrot and sauté until tender, about 7 minutes. Add the ground duck to the pan and continue to cook over medium heat until browned, 5 to 7 minutes. Pour the Marsala into the pan and cook until reduced to dry.
Add the shredded duck meat to the pan with the ground duck. Add the white wine, the chopped tomatoes and their juices, and a cheesecloth containing the remaining thyme, bay leaf, and 1 sprig of parsley. Cook until the wine has reduced by half. Season with salt and pepper and the cinnamon.
On a clean work surface, form a well in the flour. Add the eggs to the center of the well and beat lightly with a fork. Add the butter and milk to the eggs, along with a pinch of salt. Gradually pull the flour into the egg mixture with the fork and mix until the dough starts to form. Knead the dough until it is smooth and elastic and not at all sticky. Cover the dough with a bowl or kitchen towel and let rest at least 30 minutes.
Divide the dough into 8 small pieces. Knead each piece of dough with a little extra flour, then, using a meat grinder (electric or manual) with the plate with the smallest holes, put the dough through the grinder, set at the lowest setting, one piece at a time. As the pasta comes out, cut each strand with scissors or a sharp knife at 6-inch intervals. Place the pasta on a sheet pan lightly dusted with flour. Put the remaining pieces of dough through the grinder in the same manner.
Bring 6 quarts of salted water to a boil. Drop the bigoli into the water and cook until tender, 5 to 7 minutes. Meanwhile, reheat the duck ragu. Drain the pasta and toss immediately with the warm duck ragu. Garnish with the chopped parsley and serve immediately.