In a large stockpot, add the chicken, onion, carrots, celery, garlic, parsley, thyme, bay leaf, peppercorns, and salt (if using). Pour enough cold water into the pot to cover the chicken and vegetables by about 1 inch.
Place the stockpot on the stove over medium-high heat and bring the mixture to a boil.
As the broth begins to boil, skim off any foam or impurities that rise to the surface using a slotted spoon or skimmer then reduce the heat to low and let the broth simmer gently for 2-3 hours. Do not let the broth come to a rolling boil, as this can make it cloudy and less flavorful.
Remove the pot from the heat. Take out the chicken and remove the meat from the bones. Discard the bones and use the chicken meat for your soup.
Use a fine-mesh strainer or colander lined with cheesecloth to strain the broth into a large bowl or another pot, discarding the solids.
Allow the broth to cool for about 30 minutes, then transfer it to the refrigerator to cool completely. As the broth cools, any remaining fat will rise to the surface and solidify, making it easy to remove and discard.
Once the broth is completely cooled, transfer it to airtight containers or resealable plastic bags. The broth can be stored in the refrigerator for up to 5 days or in the freezer for up to 6 months.