Strip down all the edible meat from the chicken bones and carcass and use for leftovers, or reserve for use in any recipe.
Place the remaining bones and carcass in a 6-quart slow cooker (if you have a smaller slow cooker, you can divide this recipe in half). Add in any remaining skin or cooking juices as you see fit.
Add the vegetables and spices right on top of the bones.
Cover the with water, leaving about 1/2" at the top so it doesn't simmer over.
Set your slow cooker on low and cook the stock for 8-10 hours. I've cooked the stock overnight, or I've started it up in the morning before heading to work. Both options turn out great!
When the stock is done, it will be clear and any remaining meat will have fallen off the bones.
Set a colander or sieve on top of an 8-quart pot and line it with cheesecloth.
Ladle the stock into the lined sieve/colander and let drain.
Discard the contents of the cheesecloth/sieve.
Let the stock cool, then refrigerate or freeze for future use. I usually try to keep on hand a variety of sizes. So, I'll set aside some 1-cup portions, some 1-quart portions, and some 2-quart portions. I'll also freeze some stock in ice cube trays when I only need a small amount for a recipe.