Heat 2 tablespoons of the oil in a heavy pan and cook the onion over a medium heat for 10 minutes, or until soft and golden. Add the garlic and cook for 2 minutes more. Stir in the tomato passata, sugar, oregano and salt and pepper. Let the sauce bubble up, then reduce the heat to low. Cover and simmer gently for 15 minutes.
Meanwhile, cut the eggplant into 1 cm (½ inch) rounds and brush both sides with oil. Heat a griddle pan over a high heat and grill the eggplant on both sides until tender and charred.
Heat the oven to 190°C (375°F/Gas 5). Spoon one-third of the tomato sauce into an ovenproof dish about 25 x 20 cm (10 x 8 inches). Sprinkle over 1 tablespoon of the parmesan cheese, then add half the eggplant slices. Repeat the layering, finishing with tomato sauce and parmesan cheese. Sprinkle over the cheese, then the breadcrumbs. Drizzle with the remaining oil. Bake for 25 minutes, or until the top is golden and the sauce bubbling. Leave to stand in the dish for 5 minutes, then serve scattered with basil leaves (if using).