In a large bowl, combine the ground meat, ricotta, egg, Parmigiano-Reggiano, gherkins and pistachios. Mix only as much as necessary, and form into balls of a 1-inch diameter.
In a large, heavy-bottomed skillet, heat the butter until it foams and subsides. Place the balls in the butter and brown on all sides. Add the stock and, if necessary, the milk so that the liquid comes halfway up the sides of the balls. Bring the liquid to a boil, reduce to a simmer and cook 15 minutes, until the meatballs are cooked through. Serve with the broth poured over.
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.
Yield: 1 1/2 quarts