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Heat grill to medium-high heat. Brush both sides of the fish with the oil and season each with 1 teaspoon of the salt and the pepper, including the cavity. Stuff the cavity of each fish with some of the basil. Grill each fish until slightly charred on 1 side, about 4 to 5 minutes. Using a heavy duty spatula, carefully turn the fish over, close the cover and continue grilling until just cooked through, about 6 to 7 minutes. Remove from the grill and immediately drizzle each fish with 2 tablespoons of vinaigrette.