Heat 2 tablespoons olive oil in a large skillet over medium heat; add onion. Cover and cook 5 minutes. Uncover and sauté 10 minutes or until onion is lightly browned. Stir in 1/4 teaspoon salt and vinegar. Set aside, and keep warm.
Stir together 2 tablespoons olive oil, basil, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Spread mixture on both sides of fish.
Brush eggplant with remaining olive oil; sprinkle with remaining 1/2 teaspoon salt and 1/2 teaspoon pepper.
Grill fish and eggplant, covered with grill lid, over high heat (400° to 500°) 3 to 4 minutes on each side or until fish flakes with a fork and eggplant slices are done.
Cut steaks in half. Serve with eggplant, onion, and Dried-Tomato Tapenade. Garnish with fresh basil sprigs.
