Preheat the oven to 450 degrees F.
Arrange the bones and vegetables on a roasting pan
Roast on the upper rack of the oven for an hour or until the bones and vegetables have a brown, caramelized color on the edges.
Drain any fat from the roasting pan.
Use some tongs to place the bones and vegetables into a large stock pot.
Scrape any bits from the bottom of the pan into the pot. You could also pour a ½ cup of hot water into the pan and scrape it around before pouring into the pot.
Add water and the vinegar to the pot covering the bones by at least a couple of inches.
Bring the uncovered pot slowly to a boil and skim the scum off the top while it comes to a boil over 30 minutes.
Cover the pot and reduce the heat to simmer. You can transfer everything into a crock pot if that’s easier to manage.
Simmer on low heat for 6 to 24 hours. The longer the better. Check the pot every now and then and skim any new scum. Add a little water if it starts to boil away.
When done, use a slotted spoon and tongs to remove the bones and vegetables and discard them or make your dog’s day.
Strain the broth through cheesecloth in a colander to clear out any large bits of vegetable or meat bits.
If you want a highly translucent broth you can filter the broth again through a coffee filter in a small colander or large strainer. Totally optional.