Place the beef marrow bones into a 10-Quart stock pot. Cover with water by no more than one inch. If you choose to use the red vermouth or fortified wine, you can omit the apple cider vinegar. Add the red vermouth or apple cider vinegar to the stock pot.
Place the beef shanks and oxtails on to a baking sheet and bake in a 425 F degree oven until the bones have browned, approximately 45 minutes to one hour. Once browned, transfer the bones from the baking sheet to the stock pot. Deglaze the baking sheet and add the drippings to the stock pot. Add additional water, if needed, to cover the bones.
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.
Next add the onions, celery, carrots, bay leaves, and peppercorns to the stock pot and fill with the stock pot with additional water, if needed, to just cover all the ingredients. Be careful not to add too much water to the stock pot. Add only enough to cover the contents.
If using a stock pot on the stovetop, bring the contents of the stock pot up to a high simmer and immediately reduce heat to low and simmer for 12 hours.
After 12 hours, turn off the stovetop. Allow broth to cool slightly and then begin to strain ingredients with a slotted spoon. Reserve ingredients to be re-used to make a second batch of broth. (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 broth from the slow cooker or 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.
Transfer the bone broth to container(s) 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 up to 6 months but 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.