Place all the ingredients into the slow cooker or stock pot. If you choose to use the white vermouth, you can omit the apple cider vinegar. Add water to the slow cooker or stock pot just to cover all the ingredients.
If using a slow cooker, turn it to the high setting for one hour, then turn it down to the keep warm setting and allow to simmer on keep warm for six hours. If your slow cooker does not have a keep warm setting, turn it down to the low setting but tilt the slow cooker lid to allow for some of the steam to escape to prevent the broth from boiling.
If using a stock pot on the stove, bring to a boil and immediately reduce heat to low and simmer for six hours.
After six hours, turn off the slow cooker or stove. Allow the broth to cool slightly and then begin to strain ingredients with a slotted spoon. Save the ingredients if you want to reuse them to make a second batch of broth.
Once all the ingredients have been strained from the broth, line a colander with cheese cloth or a flour sack towel and place over a deep pot. Use a ladle to transfer the broth from the slow cooker or stock pot into the lined colander. The broth will drain through the lined colander into the deep pot.
Once all the 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. Transfer the broth to one or more containers with a cover 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 6 months. In a separate freezer that is not opened frequently, it will stay fresh for up to 12 months.