Begin by placing the leftover chicken, skin, juices, and chicken carcass into a large dutch oven.
Place the rest of the ingredients into the dutch oven and cover.
Heat the dutch oven over high heat and bring to a boil.
When the water comes to a rolling boil, turn the heat to low and let the chicken broth simmer on low for 4-6 hours (the longer the simmer the more flavorful the broth).
Check the chicken broth every 1 ½ hours and scrape any foam or fat that gathers at the top of the dutch oven.
When the chicken broth is done, remove the dutch oven from the heat and discard the larger chunks of vegetables and the chicken carcass.
Finally, pour the remainder of the chicken broth through a sieve and into a large jar or bowl. Discard any chunks in the sieve.
Use the chicken broth for a soup or let the chicken broth cool completely before pouring the broth into mason jars or any other airtight container.
Place the broth in the refrigerator for up to 7 days or in the freezer for up to 3 months.