Method:
Preheat oven to 375°F. Arrange tomatoes on a large rimmed baking sheet in a single layer. Drizzle with 2 tablespoons of the oil and season with salt and pepper; set aside. Arrange eggplant on a second large rimmed baking sheet, drizzle with 2 tablespoons of the remaining oil, season with salt and pepper and spread out in a single layer. Roast tomatoes and eggplant, rotating trays halfway through, until tomatoes are softened and beginning to char and eggplant is browned and softened, 30 to 40 minutes; set aside.
In a large, deep skillet, heat remaining 1/4 cup oil over medium heat. Add garlic and cook, stirring frequently, until the garlic starts to brown, about 1 minute. Add wine and simmer until reduced by about half, 8 to 10 minutes.
Meanwhile, bring a large pot of salted water to a boil. Add pasta and cook until al dente.
Add tomatoes, eggplant and olives to the garlic-wine mixture in skillet. As soon as the pasta is cooked, drain and add to skillet along with 1 or 2 tablespoons of the starchy pasta cooking water. Toss to combine well. Add ricotta salata, Pecorino Romano, basil, salt and pepper and toss gently to combine. Serve immediately.