Heat a wok over high heat. When wok begins to smoke, add one tablespoon of the peanut oil. Add carrots and green beans and stir-fry for a minute, splash in two tablespoons stock to facilitate cooking and stir-fry for another minute. Transfer to a plate and set aside.
Wipe wok dry and return to heat. When wok is hot add remaining two tablespoons oil. Add garlic, ginger, and half of the chilies and stir-fry for less than one minute. Add curry paste and stir-fry for one to two minutes. Add kaffir lime leaves and chicken and stir-fry two to three minutes until chicken has browned. Add coconut milk and stir-fry for one minute.
Stir in the 60ml stock, shiitake mushrooms, the light parts of the spring onion, bean sprouts, and fish sauce and cook for one to two minutes more or until chicken has cooked through. Add the green beans and carrots back in and season to taste with salt and white pepper. Transfer to a serving plate and garnish with remaining chilies, some bean sprouts, spring onions (green parts) and coriander.