Combine the canola oil, fish sauce, garlic, Thai chiles, and turmeric in a Vitamix or food processor and process until pureed. Brush the marinade onto the fish, inside and out. Set aside for half an hour.
Grill the fish over medium-high heat, skin side first. After 4 minutes, or once the skin is brown and blistered, flip it. Continue to cook, skin side up, until the fish is barely cooked through, about 4 more minutes.
Transfer to a platter. Garnish lavishly with the herbs and drizzle with the olive oil. Serve immediately with the lime wedges.