In this popular Southern coast technique, the scales are left on to prevent sticking and preserve moisture in the fish while capturing the blazing heat and flavor of live fire.
Heat grill to high (450°F to 550°F). Sprinkle snapper flesh with salt and pepper. Oil cooking grate liberally. Place snapper, skin side down, on grill. Cover and grill until fish flakes easily with a fork, 12 to 16 minutes. Transfer to a serving platter. Drizzle with 1/4 cup olive oil, and top with herbs and celery leaves.