Preheat the oven to 375 degrees F.
Rinse and dry the shanks and season aggressively with salt and pepper. In a heavy-bottomed Dutch oven with a lid, heat the oil until smoking. Add the shanks and sear until dark golden brown over medium heat, about 15 to 18 minutes. Remove the shanks and set aside.
To the same pan add the onion, garlic, rosemary and artichokes and cook until softened, about 8 to 10 minutes. Add the olives, wine, tomato sauce and chicken stock and bring to a boil. Replace the lamb shanks in the pan and return to a boil. Cover tightly and roast in the oven for 1 1/2 hours, until fork-tender. Remove from the oven and serve immediately.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds one week in the refrigerator or up to 6 months in the freezer.
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 3 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.
Recipe copyright 2000, Mario Batali. All Rights Reserved.