Put the eggplant on a large rimmed baking sheet and drizzle with 1/4 cup of the olive oil. Sprinkle with 1 teaspoon salt and toss together to coat the eggplant with the oil. Bake 25-30 minutes, until the eggplant is tender and golden brown.
Meanwhile, place a large (12-inch) skillet over medium heat. Add the remaining 2 tablespoons olive oil and the onion. Cook about 5 minutes to soften the onion.
Stir in the garlic, fresh and dried crushed chili pepper, tomatoes and 1/2 teaspoon salt. Cook at a simmer until the tomatoes give up their liquid and then reduce to a chunky sauce - this should take about 10 minutes.
While the tomatoes simmer, bring a large pot (4-6 quarts) of water to a boil and add 3 tablespoons salt. Cook the pasta according to package directions, or until al dente.
Drain the pasta. Lower the heat under the tomatoes, then stir in the pasta and eggplant until blended with the sauce.
Transfer to a serving dish and top with the basil leaves and cheese. Serve and enjoy!
Eggplant can be baked up to 2 days ahead - store in the refrigerator in a covered container.