Place the chicken in your largest stock pot. Add the carrots, celery, onion, bay leaf, garlic, parsley, thyme and peppercorns. Pour in the cold water and salt, adding more water (if necessary) to cover the chicken. Bring to a boil. Lower the heat; cover the pot (leaving just a small gap to allow some steam to escape). Simmer for 1 ½ hours, skimming the top occasionally.
Turn off the heat and remove the chicken from the pot. When the chicken is cool enough to handle, remove the meat from the skin and bones. Save the meat to use in a recipe and discard the skin and bones. Strain the contents of the pot through a colander into a large bowl or other pot; discard the solids. Pack the broth in containers and refrigerate for 3-4 days or freeze for up to 6 months.
Notes
The longer you simmer the broth, the richer the flavor. This is a lighter broth, which I simmered for 1 ½ hours. If you like, you can simmer the broth for up to 5 hours; however, remove the chicken from the pot after 90 minutes to prevent the meat from drying out.
As the broth is simmering, occasionally skim the foam off of the top. Skimming off the scum and fat that accumulates on the surface of the broth helps create a clear, clean broth.
Allow the broth to cool completely before packing and storing in the refrigerator or freezer. If you have time, chill the broth in the refrigerator overnight and then scrape off the surface fat before freezing or using.