Place the chicken carcasses and the feet into a 10-Quart stock pot. If you choose to use the white wine or white vermouth, you can omit the apple cider vinegar. Add the wine, vermouth or apple cider vinegar to the stock pot.
Next, add the onions, celery, carrots, bay leaves, and peppercorns to the stock pot. Fill the stockpot with water to cover the contents by no more than one inch. Be careful not to add too much water to the stock pot. Add only enough to cover the contents! It is better to error on the side of less water than too much water.
Bring the contents of the stock pot up to a boil, and once up to a boil, immediately turn the heat down to low. Skim off any foam that rises to the top. And now allow the contents to simmer for six hours.
After 6 hours, turn off the stovetop. Allow bone broth to cool slightly and then begin to strain the ingredients with a slotted spoon. Reserve chicken feet to be reused to make a second batch of bone broth if there is visible cartilage on the feet that has not dissolved. (See video for additional details.)
Once all the ingredients have been strained from the bone broth, line a colander with cheesecloth or a flour sack towel and place over a deep pot. Use a ladle to transfer the broth from the stock pot into the lined colander. The bone broth will drain through the lined colander into the deep pot.
Once all the bone broth has been strained through the lined colander into the deep pot, transfer this pot to the refrigerator until the fat rises to the top and congeals. Skim off this fat and transfer it to a separate container to be used in other recipes. Alternatively, you could use a fat separator to remove the fat at this stage. (See the blog post for recommended kitchen items.)
Transfer the bone broth to one or more containers with covers that can then be refrigerated or frozen. You can store the broth in multiple smaller containers or one single large container depending on how you plan to use it. This bone broth will stay fresh for 3-4 days when refrigerated. If frozen in the freezer of a refrigerator, it will stay fresh for up to 6 months, but it is best used within 2-3 months to prevent freezer burn. In a separate freezer that is not opened frequently, it may stay fresh for up to 12 months.