Heat grill. In small bowl, combine basil, 2 teaspoons oil and 1 garlic clove; mix well. Rub on both sides of tuna steaks. Set aside.
In food processor bowl with metal blade, combine all sauce ingredients except parsley. Process with on/off pulses until finely chopped, scraping down sides of bowl if necessary. Set aside.
When ready to grill, place tuna on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 8 to 12 minutes or until fish flakes easily with fork, turning once. Serve sauce over tuna. Sprinkle with parsley.