Put the coconut milk, lemon grass, galangal, shallots and peppercorns in a saucepan over a medium heat and bring to the boil.
Add the chicken, fish sauce and sugar or honey and simmer, stirring constantly, for 4–5 minutes or until the chicken is cooked.
Cut the mushrooms in half if large and discard any hard stems, then add to the saucepan and simmer for another 2–3 minutes. Add the lime juice, kaffir lime leaves and chillies. Taste and adjust the seasoning (this dish is not meant to be overwhelmingly hot, but to have a sweet, salty and sour taste). Add the cherry tomatoes in the last few seconds, taking care not to let them lose their shape.
Spoon into a serving bowl and garnish with a few coriander leaves.