Preheat the slow cooker if necessary; see the manufacturer's instructions. Put chicken breast side down into the slow cooker pot. Add the onion, carrots, ginger, garlic, chilli and star anise and spoon over the soy sauce, vinegar and sugar.
Pour over the boiling water. Cut the coriander leaves from the stems; add the stems to the pot, reserving the leaves. Season, cover with the lid and cook on high for 5–6 hours or until the juices run clear when the thickest part of the leg is pierced with a knife.
When almost ready to serve, put the noodles into a large bowl, cover with boiling water and leave to soak for 5 minutes. Lift the chicken out of the slow cooker pot, put on to a plate, cover with foil and keep hot. Add the mangetout and pak choi to the pot, replace the lid and cook, still on high, for 5–10 minutes or until just wilted.
Carve the chicken into bite-sized pieces. Drain the noodles, divide between 4 bowls. Top with chicken and chopped coriander leaves, then ladle over the hot broth.