1 Prepare the eggplant: Turn on the broiler and slide a rack 10-inches below the broiling element. Trim the stem and bottom from the eggplant and cut it into 1-inch pieces. Combine the eggplant and onion in a bowl and toss with salt, pepper, and 2 tablespoons of the olive oil.
2 Broil the eggplant: Spread the eggplant and onions on a large rimmed baking sheet. Broil for 5 to 6 minutes, turning once, or until the eggplant begins to char at the edges.
3 Roast the eggplant until tender: Place the eggplant and onion in the middle of the oven and turn the oven temperature to 450F. Continue roasting for 20 minutes, turning several times, or until the eggplant and onion are tender.
4 Prepare the tomato sauce: In a large pot (big enough to hold the eggplant later), heat the remaining 2 tablespoons olive oil over medium-high heat. Add the garlic and celery and cook, stirring, for 1 minute.
Crush the whole tomatoes in a bowl using your hands or a potato masher until you have small, bite-sized pieces. Add both the tomatoes and the roasted eggplant mixture into the pan with the garlic and celery. Bring to a boil, then lower the heat, cover the pan, and simmer for 5 minutes.
5 Stir the raisins, vinegar, capers, and sugar into the sauce. Continue cooking for 5 minutes, or until the eggplant is very soft. Taste for seasoning and add more salt and vinegar, if you like.
6 Cook the pasta: Bring a large pot of salted water to a boil. Add the pasta and let it cook, stirring once or twice, for 8 minutes, or until it is tender but still has some bite. Before you drain the pasta, use a heatproof measuring cup to scoop out roughly 1 cup of the water; set aside. Drain the pasta and return it to its cooking pot. Sprinkle with olive oil and toss gently.
7 Combine the pasta and sauce: Pour the eggplant sauce over the pasta, then add 1/2 cup of the pasta cooking water.. Place over low heat and stir until the sauce begins to coat the pasta. Add enough of the remaining cooking water to make a saucy mixture. Taste for seasoning and add more salt and vinegar, if you like.
8 Serve the pasta: Spoon the pasta and sauce into 4 shallow bowls. Sprinkle with Parmesan, olives, and parsley.