Once you're done feasting on your chicken, or once you've removed all the meat from the carcass, return the bones and skin to the Dutch oven, along with any and all vegetable scraps. Make sure that you also leave all the good stuff that was already in the Dutch Oven right where it sits.
Add enough water to completely cover the chicken bones, about 8 to 10 cups should suffice, as well as a tablespoon of apple cider vinegar, to help draw more of the good stuff from the bones.
Cover and place the Dutch oven in a 325°F oven and bake for 5 to 6 hours, or until your water has turned into the most delicious, richest and darkest chicken broth.
Remove the larger pieces with a slotted spoon; place them in a colander set over a large bowl to collect the excess juices. Then, strain the broth through a fine meshed sieve.
Press down hard on the larger pieces you removed earlier to help extract as much of those juices as you possibly can and add those juices to the rest of the broth, straining them through the fine mesh sieve if necessary.
Place the broth in the refrigerator until fully set and then remove as much or as little of the fat layer as you want (save this fat for cooking)
The broth will keep for about 5 days in the refrigerator and up to a few months in the freezer. Note that this broth is extremely concentrated, so you will most probably want to dilute it when you use it.