How to Make It
In a large pot, bring the chicken stock to a simmer. Add the chicken and return the stock just to a simmer. Cover the chicken with a small plate to keep it submerged and cover the pot. Reduce the heat to maintain a very low simmer; simmer until the chicken is cooked through, about 1 1/2 hours. Remove the chicken and let cool slightly, then shred the meat; discard the skin and bones. Strain the soup into a heatproof bowl. Skim off the fat and return the soup to the pot.
In a large bowl, combine the matzoh meal, salt, garlic, baking powder and baking soda. In a medium bowl, whisk the 2 whole eggs with the 3 yolks, schmaltz and onion. In a separate bowl, beat the 3 egg whites with an electric hand mixer until stiff peaks form. Stir the schmaltz mixture into the dry ingredients, then stir in one-third of the beaten egg whites until incorporated. Gently fold in the remaining whites until no streaks remain. Press a sheet of plastic wrap directly onto the surface of the batter and refrigerate for about 20 minutes or overnight, until firm.
Line a baking sheet with plastic wrap. In a small bowl, combine the vegetable oil with 1 tablespoon of water. Scoop 1-tablespoon-size mounds of the matzoh batter onto the baking sheet. Using the oil-and-water mixture to keep your hands moist, roll each scoop of batter into a ball, handling them as gently as possible.
Return the chicken soup to a simmer. Add the carrot, celery, onion, rutabaga, dill and parsley and season with a big pinch each of salt and pepper. Add the matzoh balls. Cover and cook over moderate heat, turning the matzoh balls a few times, until they are plump and cooked through, about 25 minutes. Stir the shredded chicken into the soup and cook just until the meat is warmed through, about 2 minutes. Remove the herb sprigs. Season the soup with salt and pepper and serve immediately.