Place chicken pieces in a large stockpot and add the carrots, celery, quartered onion, parsnip, garlic, fresh dill, parsley, bay leaves, peppercorns, and 1 tablespoon kosher salt. Pour in 12 to 14 cups of cold water, making sure everything is fully submerged.
Bring the pot to a boil over medium-high heat, then use a ladle to skim off any gray foam that rises to the surface. Continue skimming every few minutes for about 10 minutes until foam mostly stops appearing.
Reduce heat to low, partially cover the pot, and simmer gently for 1 hour 15 minutes to 1 hour 30 minutes. Do not allow the broth to boil hard — a slow, gentle simmer is essential for a clear, rich broth.
While the broth simmers, whisk together the eggs, schmaltz (or oil/butter), and cold seltzer in a large bowl. Add the matzo meal, salt, pepper, garlic powder, and fresh herbs if using, and stir gently until just combined — do not overmix.
Cover the matzo ball mixture with plastic wrap and refrigerate for at least 30 minutes. This step is required — chilling allows the matzo meal to absorb moisture and helps the balls hold their shape during cooking.
Remove the pot from heat and pour the broth through a fine mesh strainer set over a second large pot, discarding all solids. If desired, pull the cooked chicken off the bones, shred the meat, and set aside. Season broth with additional salt to taste.
Bring a separate large pot of salted water to a rolling boil. With lightly wet hands, gently roll 2-tablespoon portions of chilled dough into loose balls and lower them into the boiling water. Reduce to a steady simmer, cover, and cook for 30 to 35 minutes without lifting the lid.
Transfer cooked matzo balls into the simmering chicken broth using a slotted spoon, add shredded chicken if using, and let rest for 5 minutes. Ladle into bowls with 2 to 3 matzo balls per serving and garnish with fresh dill.