Combine chicken stock, lemon juice, lemon zest, garlic, lime juice, lime zest, peppercorns, soy sauce, ginger, fish sauce and chilli pepper in a large pot.
Remove tough outer stalks from lemongrass. Halve inner stalks and cut into 7.5cm pieces. Place in a resealable food bag and pound with a hammer until bruised. Add water into the bag and pour into the pot.
Bring soup to the boil; reduce heat and simmer until flavours combine, about 20 minutes. Pass soup through a sieve and discard solids. Pour strained soup back into the pot.
Stir chicken, spring onions, carrot, cabbage, bean sprouts, mushrooms, coriander, basil and mint into the soup. Simmer over medium heat until carrots are tender, about 10 minutes.
Spoon 1 teaspoon garlic chilli paste into the bottom of each serving bowl and ladle soup on top.