Remove any giblet packet from the chicken. (Optional: roast the chicken, backs, and bones first for a deeper, browner stock.) Put the chicken, backs, and bones in the pot.
Add the vegetables, seasonings, and water.
Cook in a 210°F oven for about 2 hours.
Pull out the whole chicken and pick off the meat for other dishes. Return the bones and skin to the pot and cook another 10 to 12 hours.
Strain through a fine-mesh strainer lined with cheesecloth. Discard the bones, vegetables, and skin.
Chill, then skim the fat. Portion into vacuum-seal bags, seal, and freeze flat so they stack. Fridge 3 to 5 days, freezer up to 6 months.