-
Heat the oil in a large pot over medium-high heat. Add the onion, ginger, and lemon zest and cook until the onion has softened, 3 to 5 minutes. Add the chicken, skin side down, and cook until just beginning to brown, 8 to 10 minutes.
-
Add the water, apple cider vinegar, and salt and bring to a boil. Reduce the heat to the lowest possible setting, partially cover the pot, and cook for as long as you would like, but at least 3 hours.
-
Transfer the chicken to a plate. Remove the bones and skin, shred the meat, and reserve for another use.
-
Pour the broth through a fine mesh sieve (lined with cheese cloth, if you have it) into a large bowl. Discard the solids. Cool to room temperature, then transfer to quart containers and refrigerate overnight. The next day, use a spoon to skim excess fat from the surface of the broth.
-
Reheat the broth until it is piping hot, then transfer to mugs and serve.