Calamarata is a little ring-shaped pasta. Other short tubular pasta, such as mezzi rigatoni or pennoni, can be substituted.
Preheat oven to 425 degrees. Divide tomatoes, eggplants, and garlic between 2 rimmed baking sheets. Drizzle with oil; season with salt. Toss to combine, then spread in a single layer. Roast until eggplants are tender and browned in spots, about 25 minutes.
Bring a large pot of water to a boil; add salt. Cook pasta 2 minutes less than instructed on package. Drain, reserving 1 cup pasta water.
Meanwhile, heat a large saute pan over medium-high. Cook sausage, breaking it into small pieces, until browned, 10 to 15 minutes. Add reserved pasta water; cook, scraping up browned bits from bottom of pan, until almost evaporated.
In a large bowl, combine eggplant mixture, sausage, olives, pasta, and cheese. Season with salt and pepper. Top with basil and serve immediately, with more cheese alongside.