Grilled Eggplant Parmesan

1. Heat 2 teaspoons of the oil in a medium nonreactive saucepan. Add the onion and cook over moderate heat, stirring, until wilted, about 3 minutes. Tie the carrot, celery and rosemary together with cotton string and add to the saucepan along with the tomatoes and their juices. Season with a pinch each of salt and pepper and simmer over low heat, stirring to break up the tomatoes, until the sauce is slightly reduced, about 25 minutes. Discard the vegetable bundle.
2. Pass the sauce through a food mill; alternatively, transfer to a food processor and process to a coarse puree. Season with salt and pepper.
3. Light a grill. Using a damp paper towel, coat the grill with the remaining 1 teaspoon of oil. Season the eggplants with salt and grill over a medium-low fire, turning once, until tender and golden brown, about 12 minutes.
4. Preheat the oven to 400°F (200°C). Spread 1/2 cup of the tomato sauce in a nonreactive 11-by-8-inch baking dish. Arrange one-third of the grilled eggplant in the dish, cover with one-third of the mozzarella and sprinkle with 1 tablespoon of the Parmesan. Make another layer using 1 cup of the tomato sauce, one-third each of the eggplant and mozzarella and 1 tablespoon of Parmesan. Top with the remaining 1/2 cup tomato sauce, the sliced eggplant, mozzarella and 2 tablespoons Parmesan. Bake in the upper third of the oven for about 30 minutes, or until bubbling hot and lightly browned on top. Sprinkle with the shredded basil and serve.

Make ahead: the tomato sauce can be refrigerated up to 3 days; reheat gently before proceeding. Pair with a bright red wine such as a Chianti Classico Riserva from Tuscany.