Heat 1 tablespoon oil in a large cast-iron skillet over high. Sprinkle fillets evenly with 1/2 teaspoon salt and 1/2 teaspoon pepper. Add fillets to pan; cook 4 minutes on one side or until golden brown. Place fillets, seared side up, on prepared baking sheet; bake at 500°F for 4 minutes or until desired degree of doneness.
Return skillet to medium-high. Add remaining 1 1/2 teaspoons oil to pan. Add shallots, and sauté 2 minutes. Add remaining 1/2 teaspoon salt, remaining 1/2 teaspoon pepper, tomatoes, and 1/3 cup basil; cook 2 minutes or until tomatoes begin to break down. Stir in vinegar, and cook 1 minute.
Place 1 fillet on each of 4 plates; top evenly with tomato mixture and remaining basil.