Preheat oven to 240°C. Line a large baking dish with aluminium foil. Coat lightly with vegetable oil. Place eggplant and tomato slices in a single layer on the foil. Brush with half the oil. Sprinkle with salt and pepper.
Roast until eggplant is softened and golden, 20 minutes. Let cool.
For the dressing, crush the garlic in a small bowl. Add the remaining oil and all the vinegar and whisk until blended. Overlap slices of tomato and eggplant on a serving plate and intersperse with basil leaves. Brush with dressing.