In a small saucepan, bring coconut milk and stock to the boil.
Add lemongrass, galangal, shallots, coriander root, lime leaves, chilli, fish sauce and sugar.
Simmer for approximately 15 minutes. Taste the mixture and add more fish sauce, chilli or sugar to suit your taste.
Blend the mixture using a stick blender or blender, then strain through a colander or sieve. Discard pulp.
Add the mushrooms and simmer for a further 2 minutes, then add the lime juice and set aside until required.
Pre-heat oven to 220ºC. Heat a little oil in a heavy-based frypan, and when it starts to smoke, place the barramundi into the pan, skin-side down. Cook for approximately 30 seconds then transfer the pan to oven and cook until the fish is ready, approximately 6 minutes (times will vary depending on the thickness off the fish).
Transfer fish to a serving bowl.
Bring the broth back to a simmer, add the sugar snap peas and simmer for another minute, ladle the broth over the barramundi and garnish with coriander, kaffir lime leaves and chilli.