Step 1Using a blender, puree the turmeric, fish sauce, garlic, chiles and oil. Brush the marinade onto the butterflied fish and set aside for 30 minutes to allow the flavors to infuse the fish.
Step 2Heat a grill or grill pan over medium-high heat until hot. Grill the fish, skin-side down, until the skin is brown and blistered, about 4 minutes. Carefully flip the fish over and continue to cook until the flesh is barely cooked through, an additional 2 to 4 minutes.
Step 3Plate the fish, garnishing with the herb sprigs and a drizzle of olive oil. Serve immediately, with lime wedges on the side.