Season the snapper fillets with salt and pepper. Preheat a saute pan with the olive oil until the oil is hot, 1 to 2 minutes. Add the snapper to the hot pan, flesh side down, and cook over medium heat 4 to 5 minutes. Turn to cook the skin side an additional 3 to 4 minutes. The fillets will curl inwards briefly, but once they have cooked for a minute, they will begin to relax and lay flat again, allowing you to cook the skin side to a crispy texture.
Lift out the snapper with a slotted spatula, leaving the juices and oil in the pan. Add the sundried tomatoes, garlic, and shallots, and saute together for 2 minutes. Add the fresh herbs to the pan. Stir quickly, just to heat the herbs enough to release their aromas. Pour the sundried tomato and herb mixture over the snapper. Then drizzle a teaspoon of basil oil over each fillet and around the dish.