Place garlic, red onion, galangal, lemongrass, fish sauce, and brown sugar in a blender and process until finely blended.
Add coconut milk and blend until combined.
Transfer coconut mixture to a heavy saucepan.
Crush kaffir lime leaves in your hand to release oils and add them to the coconut milk mixture.
Heat to a gentle simmer and cook for 10 minutes allowing the flavors to infuse and the sauce to reduce slightly. Add lime juice.
Strain and simmer before adding the fish. Gently poach fish for 4-5 minutes.
Check for taste and add salt, pepper, and lime juice as desired.