Place the chickens, onions, carrots, celery, parsnips, parsley, thyme, dill, garlic, and seasonings in a 16- to 20-quart stockpot. Add 7 quarts of water and bring to a boil. Simmer, uncovered, for 1 hour. Remove 2 of the chickens and allow to cool slightly. Remove the breast meat from both chickens and set aside. Return the remaining chicken and carcasses to the pot and continue simmering, uncovered, for 3 more hours. Strain the entire contents of the pot through a colander and chill. Remove the surface fat, then reheat the stock as follows, or pack in containers and freeze.
For matzo Balls whisk together the egg yolks, chicken stock, chicken fat, parsley, and salt. Stir in the matzo meal. In the bowl of an electric mixer with a whisk attachment, whip the egg whites with a pinch of salt until they are stiff. Whisk them into the matzo mixture until it is smooth. Refrigerate for at least 15 minutes, or until the mixture is thick.
Form balls the size of golf balls by shaping them with 2 spoons, rolling them with your hands, or scooping them with a small ice cream scoop. Drop them into simmering chicken stock and cook for 30 minutes, or until fully cooked and puffed, turning once. Remove and serve hot in chicken soup.
To serve the soup, return the stock to the pot and reheat, adding the diced carrots, celery, dill, and parsley. Shred the reserved chicken breast meat into large pieces and add to the stock. Simmer over low heat for 5 minutes to cook the vegetables and reheat the chicken. Season to taste and serve as is, or ladle each serving over 2 warm Matzo Balls.