Make the soup: Place the quartered chicken, necks or feet (if using), onions, celery, parsley root or parsley, carrots, turnip, parsnip, peppercorns, star anise, and salt in a 12-quart stock pot. Add 5 quarts (20 cups) of cold water and set over high heat to boil, about 30 minutes.

Turn down the heat to a simmer, set the cover ajar on top of the pot, and allow to cook for 2 hours, using a large spoon to skim off any scum that rises to the surface.

Add the dill and simmer an additional 45 minutes.

Turn off the heat and allow to cool.

When cool enough to handle, ladle the soup through a fine sieve into storage containers. Chill overnight. Remove any fat that congealed on the top of the soup and store for up to two days or freeze until ready to use.

Make the matzo balls: Combine the eggs, salt, schmaltz and soup or water in a mixing bowl and whisk until blended.

Using a fork, stir in the matzo meal and mix until smooth. Let set in the refrigerator for 30 minutes, until the matzo meal absorbs the liquid and the mixture sets near firm.

In a large pot, bring your chicken soup to a simmer. In a separate pot, bring about 5 quarts of water to a boil with 2 tablespoons of kosher salt.

Remove the matzo ball mixture from the fridge. Wet your hands with cold water and shape a heaping tablespoonful of the mixture into a ball in the palm of your hands. Coax the matzo ball into a sphere. Rolling it too tightly will prevent it from achieving its puffiest. Drop into the boiling water and repeat with the remaining mixture, cleaning and wetting your hands as necessary to keep the matzo balls from sticking to your skin. Be careful not to crowd the pot you are cooking the matzo balls in or they will not cook through fully.

Bring the pot back up to a boil, turn down the heat to a simmer, cover tightly and cook for an additional 35 to 40 minutes, until the matzo balls have risen from the bottom of the pot and have blown up to about twice their original size. Occasionally a matzo ball or two will stick to the bottom of the pot. Give it a nudge with a spoon to loosen.

While your matzo balls cook, make the vegetable garnish: Add the sliced carrots and diced turnip to the simmering pot of soup, and cook for 30 minutes. Add the celery and cook about 15 more minutes, until all of the vegetables are tender. Add the dill. Keep warm until ready to serve.

Using a slotted spoon, remove the matzo balls from the boiling water and place them directly into the simmering chicken soup. Or, if preparing in advance, remove them from the cooking liquid and let them drain on a cookie sheet. Freeze them on the sheet until they are firm, and then transfer them to a resealable plastic bag. Defrost them in simmering soup directly from the freezer.

To serve, transfer the matzo balls to bowls and ladle the soup and vegetable garnish over top.