Warm the olive oil in a large, heavy casserole and cook the speck until light golden brown. Remove it to a plate, using a slotted spoon. Season the chicken with salt and pepper and brown it on both sides, then remove it to a plate. Add the leeks and shallots and saute. Add the thyme, bay leaf, wine, and chicken stock, scraping the bottom of the pot with a wooden spoon to dislodge the browned bits. Bring to a simmer and return the chicken to the casserole.
Cover the casserole loosely and simmer for 30 minutes. Add the soaked prunes and their liquids and simmer another 30 minutes, until the chicken is very tender and falling off the bone.
Remove the chicken to a plate and add the sauteed speck. Reduce the sauce for 5 minutes and season with salt and pepper. Return the chicken and speck to the sauce, let rest to cool, then reheat gently and serve.
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.