Heat the peanut oil in a large wok over high heat. Add garlic, ginger and half the chilli. Cook for 30 seconds and then add half the stock. Bring to the boil and reduce heat to low.
Add chicken to wok and cook for about 3 minutes or until cooked through. Remove the chicken with a slotted spoon and set aside, covered, to rest. Add the remaining stock, soy sauce, sesame oil and sugar to the wok and bring to the boil.
Add the bean shoots, bok choy and pak choy and cook for a further minute or until just wilted. Remove from the heat and ladle over the noodles. Wait 2-3 minutes.
Separate the noodles with a fork, and top with the chicken and shallots. Serve with a wedge of fresh lime.