How to Make It
Make the pickled carrot and jalapeño: Stir together all ingredients in small bowl. If the vegetables are not just covered by liquid, add extra vinegar and water in a 1:1 ratio with an extra pinch of salt and an extra pinch of sugar. Let stand at room temperature at least 1 hour and up to 4 hours.
Make the broth: Depending on the size of the turkey parts, break them up into pieces that will fit into a 6-quart programmable pressure multicooker (such as Instant Pot). Quickly spray or rinse off impurities from the roasted pieces, especially in the backbone wells. Put all turkey parts in cooker, and add onion, apple, ginger, salt, star anise, and 9 cups water. Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select high pressure for 40 minutes. (It will take 15 to 20 minutes for cooker to come up to pressure before cooking begins.) Let the pressure release naturally for 20 minutes. Remove lid from cooker. (Times, instructions, and settings may vary according to cooker brand or model.)
Meanwhile, place mushrooms in a medium bowl; add 1 cup boiling water, and let soak until mushrooms are softened, about 15 minutes. Drain in a fine wire-mesh strainer set over a small bowl; reserve soaking liquid. Trim shiitake stems if they are big, then quarter caps. Put trimmed mushrooms in a 4-quart saucepan, and add reserved soaking liquid.
Using tongs, remove turkey parts from cooker. Pick turkey meat for serving, if you like, or save for another use.
Position a fine wire-mesh strainer over saucepan with shiitake mushrooms; line strainer with muslin or cheesecloth for a super-clear broth. Pourbroth throughlined strainer; discard solids. Using a ladle, skim fat from top of broth; discard. (You will have about 9 cupsbroth.) Stir in Chinese five spice and soy sauce. Bring stock mixture to a simmer over medium.
Make the soup: While broth comes to a simmer, divide noodles among 6soup bowls. Arrange roastturkey meatevenly on noodles in a single layer. (If the noodles and chicken are cold, reheat them in the microwave.) Top evenly with scallions and cilantro.
Add bok choy to simmering broth, and cook, stirring constantly, until bok choy leaves are bright green and stalks are crisp-tender, about 1 minute. Stir in salt, adding more to taste, 1/4 teaspoon at a time. Divide broth and vegetables among bowls. Drizzle with sesame oil or chile oil, and sprinkle with pepper. Serve with pickled carrot and jalapeño along with the pickling liquid for bright flavor.