Adjust the oven rack to the middle position and heat the oven to 400°F. Toss the eggplant with oil on a greased rimmed baking sheet, season with salt and pepper, and roast until golden brown and tender, about 30 minutes, stirring occasionally to ensure even browning.

Bring a large pot of salted water to a boil. Add the pasta and cook, stirring often, until nearly al dente—the pasta should be slightly firm to the bite as it will finish cooking in the oven. Reserve some cooking water, then drain the pasta and set it aside.

Wipe out the pot used for the pasta, add oil, garlic, and pepper flakes, and cook over medium heat until the garlic is fragrant. Stir in the tomatoes and salt, then simmer until the sauce has thickened slightly, about 10 minutes.

Remove the pot from the heat and stir in the cooked pasta, reserved cooking water, and roasted eggplant. Use a spoon to break up any pasta clumps and season with salt and pepper to taste.

Mix the ricotta, oil, salt, and pepper in a medium bowl until thoroughly combined.

Transfer half of the pasta mixture to a 13 by 9-inch baking dish. Place large dollops of the ricotta mixture over the surface, then top with the remaining pasta. Sprinkle the mozzarella and Parmesan evenly over the top.

Bake until the sauce is bubbling around the edges and the cheese is melted and spotty brown, about 25 minutes. Allow the dish to rest for 10 to 15 minutes before sprinkling with basil and serving.