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Boil the kettle. Remove the chicken skin, then shred the meat and discard the bones. Set aside. In a large pan, toast the sesame seeds for 1 min until golden, then tip into a large bowl (big enough to hold the noodles).
Fill the pan with water from the kettle and bring back to the boil. Add the noodles and cook following pack instructions. Tip in the beans and broccoli for the last 2 mins.
Meanwhile, mix the tahini, sesame oil, honey, soy sauce and vinegar into the sesame seeds. Drain the noodles, reserving a cup of the cooking water, and run under cold water to cool. Drain again and toss through the sauce along with the chicken. Add a splash of the cooking water to make the sauce thin enough to coat the noodles (it will thicken as it cools). Transfer to containers and chill until ready to eat, if not eating straight away.