On a clean work surface, mound 3 1/2 cups of the flour, reserving 1/2 cup. Form a well at the center of the mound and place the eggs, salt, and olive oil in the center of the well. Beat the wet ingredients with a fork and slowly drizzle in the warm water. Start to incorporate the flour into the center of the well, a little at a time, until it is all incorporated.
With clean, floured hands, knead the dough for 20 minutes by hand, or use the dough hook attachment in a mixer. The dough should be smooth and satiny.
Let rest for 2 hours, covered and refrigerated, before rolling out.
Cut the dough into thirds or quarters, and roll out to the second-thinnest setting on a pasta rolling machine.
Cut the pasta into 1 1/2-inch thick strips, then lay the strips atop one another forming 3 stacks.
Cut the strips crosswise at a slight angle at 2-inch intervals, forming lozenges.
Roll each lozenge into a quill shape, pressing the ends together as they overlap. Set aside on a baking sheet, covered with a damp towel.
In a large casserole, combine the onion, pancetta, and olive oil and cook over high heat until the onion is golden. Season with salt and pepper, to taste.
Add the carrot, bay leaves, cloves, and rosemary. Season well with salt and pepper, then push the aromatics to 1 side of the pot.
Season the meat with salt and pepper and add to the pot. Cook over high heat until it is browned on all sides, about 15 minutes.
Add the tomato paste and stir it in thoroughly.
Add the wine and simmer for 30 minutes.
Add the tomatoes and stock, stir them in thoroughly, then simmer for 3 hours, or until the meat is very tender.
Remove the meat and set aside. Once the meat is cool enough to handle, shred it with a fork. Return the meat to the pot and simmer for another 30 minutes, until it is a nice thick ragu consistency.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Cook the pasta quills in the boiling water until tender yet al dente, about 4 minutes.
Drain and toss in a large serving bowl with enough ragu to coat the pasta but not overwhelm it.
In a large, heavy-bottomed saucepan, heat the oil over high heat until smoking.
Add all the chicken parts and brown all over, stirring to avoid burning.
Remove the chicken and reserve.
Add the carrots, onions, and celery to the pot and cook until soft and browned. Return the chicken to the pot and add 6 quarts of water, the tomato paste, peppercorns, and parsley. Stir with a wooden spoon to dislodge the browned chicken and vegetables bits from the bottom of the pan. Bring almost to a boil, then reduce heat and cook at a low simmer until reduced by half, about 2 hours, occasionally skimming excess fat.
Remove from heat, strain, and press on the solids with the bottom of a ladle to extract out all liquids. Stir the stock to facilitate cooling and set aside. Refrigerate stock in small containers for up to a week or freeze for up to a month.
