For the chicken soup: Bring the chicken stock to a simmer in a large pot. Add the chicken and return the pot to a simmer. Place a plate on top of the chicken to keep it submerged and then cover the pot with a lid. Lower the heat and simmer until the chicken is done, about 1 1/2 hours. Remove the chicken from the pot, then pull the meat off and shred it. Discard the skin and bones. Strain the soup into a heatproof bowl. Skim off the fat and return the soup to the pot.
For the matzo balls: In a large bowl, combine the matzo meal, salt, baking powder, baking soda and granulated garlic. In a medium bowl, whisk the 2 whole eggs and 3 egg yolks, the chicken fat and the onion. In a separate bowl, beat the 3 egg whites with an electric mixer until stiff peaks form. Stir the chicken fat mixture into the dry ingredients, then stir in one-third of the beaten egg whites until incorporated. Gently fold in the remaining whites until there are no remaining streaks. Press a sheet of plastic wrap directly onto the batter and refrigerate for about 20 minutes or overnight, until firm.
Line a baking sheet with plastic wrap. Combine the vegetable oil with some water in a small bowl to keep your hands moist. Scoop 1 heaping tablespoon of the matzo ball mixture into your hands and form into a mound. Place the mound on the prepared baking sheet and repeat with the remaining matzo ball mixture. Use the oil and water mixture to keep your hands moist while you roll each scoop of batter into a ball. Handle the balls as gently as possible.
For the finishing touches: Return the chicken stock to a simmer and add the celery, carrot, onion, rutabaga, dill, parsley and a pinch of salt and pepper. Add the matzo balls. Cover and cook over moderate heat, turning the matzo balls a few times, until they are plumped and cooked thoroughly, about 25 minutes. Stir in the shredded chicken and cook until the chicken is heated, about 2 minutes. Remove the dill and parsley sprigs. Season with salt and pepper and serve immediately.
This recipe has been updated and may differ from what was originally published or broadcast.