1 Trim both ends of lemongrass and peel tough outer layer. Peel ginger root. Cut lemongrass and chile into small pieces and combine with 450 ml (approximately 2 cups) of salted water in a pot. Rinse chile pepper, wipe dry and add to pot. Bring to boil, then reduce heat and cook for about 3 minutes. Let cool.
2 Pour lemongrass mixture through a fine sieve, reserving broth.
3 Rinse cilantro, shake dry, pluck leaves and finely chop. Combine in a shallow baking dish with the cooled broth. Cover and freeze for 4-5 hours.
4 Peel onions and garlic and chop finely. Peel cucumber and cut into 1 cm (approximately 1-inch) pieces.
5 Cut bell pepper into quarters, remove seeds, rinse and pat dry. Cut pepper into 1 cm (approximately 1/2-inch) pieces.
6 Heat oil in a pot over medium heat. Cook onions and garlic until translucent. Add cucumber and bell pepper and cook until softened, about 3 minutes more.
7 Pour in chicken stock and coconut milk, bring to a boil and cook over medium heat for 10-15 minutes.
8 Rinse mint, shake dry, pluck leaves and coarsely chop. Puree soup with an immersion blender.
9 Squeeze juice from lime and add to soup along with fish sauce. Season with salt and pepper. Allow to cool and then chill in refrigerator for 3-5 hours. Meanwhile, transfer lemongrass broth to an ice-cube tray and freeze until firm, then place in freezer bags, wrap in a kitchen towel and crush with a meat mallet. To serve, divide soup and lemongrass ice among chilled bowls.