Place chicken giblets and carcasses into a big stock pot. Add enough water to cover the bones (approximately 1 gallon) and the apple cider vinegar.
Cover and bring to a boil on top of the stove, then turn down the heat to keep a low simmer for 24-48 hours. Stir once or twice in the first few hours, and then stir at least a couple of times over the next couple of days.
Add the vegetables, garlic, salt and bay leaves to the pot. Increase heat to bring back up to a boil, then cover and reduce heat to maintain a simmer.
Cook for 4-8 hours more, stirring every hour or so. Let simmer with lid off for the last 2-3 hours.
Strain all the ingredients by pouring bone broth from one pot to another through a colander or strainer.
Place the pot containing the strained broth in a sink with water and ice to bring the temperature down quicker. Then pour the cooled broth into storage containers. Once cooled overnight remove and throw away fat cap.
