Place the chicken, onion, garlic, carrots, celery, parsley, kosher salt, black peppercorns, and water in a large, heavy-bottomed stockpot. Bring to a boil. It should take about 20 minutes for the water to reach a boil.
Skim the foam layer from the top with a spoon, then reduce the heat to medium-low.
Partially cover the pot and simmer the broth for 3 hours. Check the soup periodically to ensure it maintains a slow, steady simmer rather than reaching a boil.
Remove the solids using a large slotted spoon.
Strain the broth through a colander. If you can’t bring yourself to discard the chicken, keep it and use it (without the skin) in these chicken patties.
You can serve the broth immediately or cool it completely and refrigerate it overnight. The next day, remove the fat layer from the top before reheating the broth.
It's important to use bone-in, skin-on chicken pieces such as chicken drumsticks or bone-in thighs. They give the broth flavor and richness. Boneless, skinless chicken breasts, for example, will not work in this recipe. They are too lean.
This broth keeps well in an airtight container in the fridge for about 5 days. You can divide some of it into individual portions and freeze them in 1-cup containers. 8-ounce mason jars work well for this purpose.