Remove the bone, most of the fat and all of the gristle from the lamb and cut the meat into 1-inch cubes.
In a large Dutch oven, combine 2 tablespoons butter, the oil, onion, thyme, bay leaves, vinegar, stock and salt and pepper, to taste, and bring to a boil over medium-high heat. Add the lamb cubes and cook, covered, for 1 hour. The meat should be very tender, and there should be very little liquid left in the pan. If there is a lot of liquid in the pan, remove the meat and reduce the liquid over high heat, then return the meat to the pan.
In a small saucepan, melt the remaining butter and mix in the horseradish and parsley. Cook, stirring, over high heat for 1 minute, then pour the sauce over the meat and toss to coat. Serve immediately.
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 2001, Mario Batali. All Rights Reserved.