Place the chicken pieces in a large stockpot, at least 8 quarts. Then add the onions, garlic, celery, parsnips, 2 of the carrots, parsley, salt, peppercorns, and cold water.

Bring everything to a lively simmer over high heat, and then lower the heat right away.

Keep the broth at a gentle, uncovered simmer for 1 hour.

While it cooks, peel the other 2 carrots and slice them thinly on a diagonal.

After the first hour, move the chicken breasts and thighs to a plate so they can cool.

Continue simmering the broth for about 1 more hour.

When the chicken is cool enough to handle, shred the meat and discard the skin and bones.

Strain the broth through a colander set over a large bowl.

Discard the solids, then return the broth to the pot. Season with salt and pepper, and skim off extra fat if you want a lighter soup.

Whisk the eggs in a bowl, then stir in the dill, matzo meal, schmaltz or butter, 2 teaspoons salt, and pepper.

For fluffy matzo balls, add the seltzer and baking powder. For denser matzo balls, use chicken broth and skip the baking powder.

Cover the mixture and chill it for at least 2 hours, or overnight if you have time.

Bring a large pot of salted water to a boil.

With wet hands, roll the chilled mixture into balls, about 1 1/2 tablespoons each, and place them on a parchment-lined sheet.

Simmer the matzo balls for about 10 minutes, until they float and are cooked through.

Meanwhile, bring the strained broth to a simmer, add the sliced carrots and shredded chicken, and cook for about 10 minutes.

Then lift the matzo balls into the soup and simmer for 5 minutes more before serving with dill and black pepper.