To make the Leftover Roast Chicken Soup in your slow cooker, see the Slow Cooker Variation below.To make the Leftover Roast Chicken Soup on your stovetop, combine the chicken carcass and any residual meat and desired aromatics in a large stock pot (5- to 8-quart capacity) and fill the pot with water so the chicken is fully submerged. Set over the lowest of low heat, lid that puppy 3/4 of the way so the water can evaporate a little bit but not too much, and leave it for at least 6 hours, skimming any scum that accumulates on the surface of the stock but leaving any puddles of fat. [Editor's Note: Christina Tosi leaves the stock simmering overnight. You may or may not wish to do the same. We guess it depends on your level of risk taking and whether your homeowner's insurance is up to date.] Remove the pot from the heat. Your kitchen smells amazing, right? Strain the liquid from the chicken into another large pot and let the solids rest in the strainer. Walk away for a little while. Brush your teeth. Brush your hair. The chicken should be cool enough to handle at this point.
Using your hands, separate the chicken meat from the bones, aromatics, and gelatin. Don’t be grossed out—put your best farm girl face on, roll up your sleeves, and get to work. This should yield 2 to 3 cups light and dark meat, depending on how much chicken you ate the night before. Toss the bones and stuff in the trash. Add the shredded chicken to the pot with the broth. (You can cover and refrigerate the soup until dinnertime.)
Bring the soup to a gentle simmer. If you want, you can clean out your fridge by throwing in a handful of baby carrots, chopped onion, Brussels sprouts, spinach, or whatever else you've got languishing in your vegetable bin. It'll taste awesome. Simmer until the soup is warmed through and any vegetables are tender.
Stir in the soy sauce, apple cider, and black pepper to taste and ladle into bowls.