Place the lemon grass, galangal, chillies and garlic in a mini blender with the measured water and blend to a smooth paste. Set aside.
Pat the fish dry with kitchen paper, arrange on a grill rack and cook under a medium-hot grill for 10–12 minutes or until cooked through.
Meanwhile, heat the oil in a nonstick frying pan and stir-fry the spice paste for 4–5 minutes. Add the coconut milk and fish sauce and cook, stirring, over a high heat for 5 minutes. Add the fish to the pan with the peanuts and basil, and toss gently to mix well. Serve immediately.