Prepare the Chicken Broth: In a large stockpot, combine the chicken pieces, quartered onions, chopped carrots, chopped celery, parsley, dill, thyme, bay leaves, peppercorns, and salt. Add the cold water, ensuring the chicken is fully submerged. Bring to a boil over high heat, then immediately reduce heat to low, cover, and simmer gently for at least 2-3 hours, or up to 4 hours for maximum flavor. Skim off any impurities that rise to the surface during the first hour.
Strain the Broth: Once the broth has simmered, carefully strain it through a fine-mesh sieve into a clean pot or large bowl. Discard the solids. You should have about 8-10 cups of rich broth. Taste and adjust seasoning with salt and pepper if needed. You can let the broth cool and then refrigerate it to easily remove the solidified fat from the top for a clearer soup, or use it as is.
Make the Matzo Ball Mixture: In a large mixing bowl, whisk together the eggs, chicken fat (or oil), and seltzer water until well combined. In a separate bowl, whisk together the matzo meal, chopped dill, chopped parsley, salt, and pepper.
Combine and Chill: Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix. Cover the bowl tightly with plastic wrap and refrigerate for at least 30 minutes (or up to 2 hours) to allow the matzo meal to absorb the liquid and the mixture to firm up.
Cook the Matzo Balls: Bring the strained chicken broth to a gentle simmer in a large pot. While the broth is heating, wet your hands with cold water and gently form the matzo ball mixture into balls about 1 to 1.5 inches in diameter. They will expand as they cook, so don't make them too large. Carefully drop the formed matzo balls into the simmering broth.
Simmer and Serve: Cover the pot and let the matzo balls simmer gently in the broth for about 25-30 minutes, or until they are puffed up and cooked through. Avoid boiling vigorously, as this can cause them to break apart. Ladle the hot broth and several matzo balls into bowls. Garnish with fresh dill or parsley, if desired.