Toss the vegetables with 3 tablespoons of the oil, arrange in a shallow roasting dish and season to taste. Place in a preheated oven, 200°C (400°F), Gas Mark 6, for 15 minutes, turning occasionally, until lightly charred.
Mix the remaining oil with the garlic and vinegar and stir into the vegetables. Arrange the tuna steaks in the dish and season well. Return to the oven for a further 12–15 minutes until the tuna is cooked. Serve immediately, scattered with the basil.