Turkisk Jook

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1. 1
   Bring 1 roast turkey or rotisserie chicken carcass, meat removed, 2 large carrots, peeled, coarsely chopped, 2 celery stalks, coarsely chopped, 1 small onion, unpeeled, quartered through root end, 3 dried shiitake mushrooms, one 2" piece ginger, peeled, sliced ¼" thick, 3 pieces chung choi (salted preserved turnip) or 1 ball, coarsely chopped (if using), and 4½ qts. water to a boil in a large stockpot or Dutch oven. Reduce heat to low, cover pot, and gently simmer, stirring and skimming foam from surface occasionally, until light golden, flavorful, and faintly fragrant, about 2 hours. Carefully strain stock through a fine-mesh sieve into another stockpot or a large bowl; discard solids. You should have 1 gal. stock. If you are short, add water to get you there. Do Ahead: Stock can be made 1 day ahead. Let cool, then transfer to airtight containers. Cover and chill.
2. 2
   Bring stock, 1⅓ cups calrose or other medium-grain rice, rinsed, ¼ cup unsalted roasted peanuts, 1 Tbsp. plus 1 tsp. Diamond Crystal or 2¼ tsp. Morton kosher salt, and 2 cups shredded or 1" pieces cooked turkey to a boil in a clean large stockpot or Dutch oven. Reduce heat to medium-high and cook until rice is just starting to fall apart, 12–17 minutes. Reduce heat to medium-low and simmer, stirring often to prevent it from burning, until rice is falling apart and mixture is creamy and thick enough that any toppings won’t sink, 1–1½ hours. Taste jook and season with more salt if needed.
3. 3
   Ladle jook among bowls and top with remaining 1 cup shredded or 1" pieces cooked turkey, then cilantro leaves with tender stems, julienned peeled ginger, thinly sliced scallions, store-bought fried onions, and/or sriracha if desired.