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Step 1
Add stock, mushrooms, scallions, garlic, and ginger to a programmable pressure multicooker (such as Instant Pot). (Times, instructions, and settings may vary according to cooker brand or model.) 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 10 to 12 minutes for cooker to come up to pressure before cooking begins.)
Step 2
When cooking cycle finishes, let the pressure release naturally for 10 minutes. Carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). (This will take 1 to 2 minutes.) Remove lid from cooker, and press CANCEL. Add kombu and bonito to stock in cooker. Let steep, uncovered, 15 minutes. Pour stock through a fine mesh strainer into a bowl. Reserve mushrooms for serving, and discard remaining solids.
Step 3
Return strained stock to cooker, and select SAUTÉ setting. Select HIGH temperature setting, and bring stock to a gentle boil. Stir in tamari and mirin, and add chicken; cook, undisturbed, until a thermometer inserted into thickest portion of meat registers 165°F, 14 to 16 minutes. Remove chicken from stock; let cool slightly, about 5 minutes. Slice diagonally into 1/4-inch-thick pieces.
Step 4
Divide cooked noodles evenly among 4 bowls. Spoon stock evenly into bowls; top with chicken, reserved mushrooms, eggs, sesame seeds, and additional chopped scallions.