Pound all the spice paste ingredients in a mortar with a pestle until you have a fine paste. Or use a blender to process the ingredients, adding
Make a few deep cuts in the thickest part of the fish. Turn over and repeat on the other side. Rub half the spice paste all over the fish and leave to marinate for 30 minutes.
Heat the vegetable oil in a wok until almost smoking. Add the remaining spice paste and stir-fry for about 5 minutes until fragrant. Add the coconut milk and lemongrass and simmer for a few minutes. Taste and adjust the seasoning with the lime juice. Remove from the heat and keep warm.
Heat a barbecue or grill until hot and cook the fish for about 5 minutes on each side, or until just cooked through. Put the fish on a serving plate, spoon the sauce over and sprinkle with coriander leaves to serve.