Step 1Place the lamb shanks on a rack over a rimmed baking sheet. Season each shank with one-eighth teaspoon salt. Place the shanks, uncovered, in the refrigerator and chill overnight.
Step 2Coarsely chop the 2 whole carrots along with the 2 whole onions and the 3 stalks celery.
Step 3Heat the oven to 350 degrees. Heat 1 tablespoon of olive oil in a large, heavy roasting pan over high heat until almost smoking. Add the shanks and brown them on all sides to a nice golden brown. When they're done, remove the shanks to a plate or baking sheet.
Step 4To the hot pan, add the coarsely chopped carrots, onions and celery, and scrape the bottom of the pan to lift any flavorings left over from the shanks. Stir in the wine, rosemary, thyme, marjoram, cinnamon stick and juniper berries. Cook over medium heat, simmering, until the liquid reduces by half, about 5 minutes.
Step 5Return the shanks to the pan, and pour in just enough chicken broth to cover the shanks. Cover the pan with enough foil to form a tight seal, then with the pan's lid.
Step 6Place the pan in the oven and cook until the meat pulls easily from the bone, about 3 to 4 hours.
Step 7Gently remove the shanks from the pan, and strain the liquid in the pan into a large measuring cup, discarding the vegetables and solids. Set the strained liquid aside.
Step 8Cool the shanks slightly, then pull the meat from the bone, shredding the meat into large pieces. Discard the tendons, and separate the meat from the fat, saving each separately. Coarsely chop the fat.
Step 9In a large saute pan, heat the butter along with 1 tablespoon olive oil and the lamb fat over medium-high heat. Cook slowly until the fat is a deep brown, and be careful as the fat will "pop" in the pan.
Step 10Stir in the finely cubed carrots, onions and celery, then add the shredded meat. Add enough of the strained liquid to cover the meat and vegetables, and season with salt and pepper to taste. Very gently simmer the meat and vegetables for 1 hour, stirring occasionally and taking care not to break the meat into smaller pieces. This makes about 8 cups ragu.
Step 11When the ragu is almost done, bring a large pot of salted water to a boil. Cook the pappardelle until it is just al dente, about 8 to 10 minutes or according to the package directions.
Step 12Strain the pasta, saving a little of the cooking liquid to stir with the ricotta. Toss the pasta with just enough ragu to dress it lightly.
Step 13Press the ricotta through a fine strainer into a medium bowl, then stir in a couple of tablespoons of the pasta liquid to give the cheese a lighter consistency, adding more liquid if desired.
Step 14To serve the ragu, spoon a little of the ricotta on each plate. Spoon over the pappardelle and ragu, and top with Parmesan cheese. Serve immediately.