Preheat oven to 400F.
Cut 4 to 5 slits on one side of the eggplant and place it slit-side-up on a baking sheet. Trim about an inch off the top of the head of garlic, just exposing the tops of the cloves inside. Place the garlic on a piece of aluminum foil, drizzle with a little EVOO, wrap it up and place it in the oven alongside the eggplant. Roast them both for about 30-40 minutes, until the eggplant looks like a flat tire.
When the eggplant and garlic only have about 15 minutes left to roast, put the grape tomatoes on a baking sheet, drizzle them with some EVOO and season with salt and freshly ground black pepper. Transfer to the oven and roast for about 15 minutes.
Place a large pot of water over high heat with a lid on it and bring up to a boil. Once boiling, add some salt and cook the pasta according to the package directions to al dente. Right before draining the pasta, remove and reserve about 1 cup of the pasta-cooking water.
Once the eggplant, garlic and tomatoes are all roasted, remove everything from the oven. Split the eggplant open and scoop out all of the roasted flesh with a spoon, discarding the skin. Transfer the flesh to a large serving bowl along with the roasted tomatoes.
Squeeze out the roasted garlic flesh from the papery shell and add to the eggplant and tomatoes. With the back of a fork or a potato masher, smash up the eggplant, tomatoes and garlic until thoroughly combined. Add some salt, freshly ground black pepper, and the reserved pasta-cooking liquid to the bowl, stirring and smashing to combine.
Add the pasta and toss to coat. Let the pasta sit for a couple minutes to absorb the flavors of the sauce. Just before serving, top with the torn basil and crumbled ricotta salata or a large dollop of the ricotta cheese. Serve with your favorite salad or Rach's Orange & Arugula Salad alongside.