Combine the chicken, vegetables, herbs, and peppercorns in a large stockpot. Pour in enough water to just cover the chicken completely. Heat the water to just under a boil over medium-high heat. Reduce the heat to a very low simmer, so that 1 or 2 bubbles break the surface of the broth about once a minute. Skim any fat and scum from the surface with a ladle, large spoon, or skimmer. (To prevent losing a lot of stock when skimming, put the skimmed liquid into a degreasing cup, and return any useable broth back to the pot.) Cook for about 1 hour or until the chicken is cooked through but not dry.
Remove the chicken from the pot, but continue to simmer the broth. Cool the chicken for about 10 minutes. Cut the chicken meat from the bone, and reserve for a chicken salad, soup, or other recipe. Return the bones to the pot and cook for 1 hour.
Strain into a non-reactive container, like another pot, a large bowl, or plastic quart or pint containers. Fill the sink with a mixture of ice and cold water so it comes about halfway up the sides of the container. Nestle the broth in the ice bath. (Stirring the broth speeds up the cooling process.) Cover and refrigerate or freeze the broth for future use. Broth can be stored in the refrigerator for up to 5 days. If the broth is unused after 5 days bring it to a boil before using.
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