Step 1

Position a rack in the middle of the oven and preheat the oven to 425 F.

Step 2

In a large bowl, whisk together red wine vinegar, sugar, 1 1/2 tablespoons tomato paste, grated garlic, 1 teaspoon salt, and 1/2 teaspoon freshly ground black pepper. Slowly stream in 5 tablespoons olive oil until emulsified. Set aside.

Step 3

On an unlined, rimmed baking sheet, toss the eggplant with crushed red pepper (if using), 3 tablespoons of the dressing, the remaining 2 tablespoons olive oil, 1 tablespoon tomato paste, 1 teaspoon salt and 1/2 teaspoon freshly ground black pepper until the eggplant is evenly coated. Arrange the eggplant in a single layer.

Step 4

Roast the eggplant on the middle rack for 12 minutes. Remove the sheet pan from the oven, add the onion and another 3 tablespoons dressing to the eggplant, toss with a heatproof spatula or tongs to coat and spread into an even layer. Continue to cook until the eggplant is fork tender and browned in spots and the onion is softened and translucent, 12 to 15 minutes more.

Step 5

Remove the pan from the oven, add the capers to the eggplant and toss. Let cool slightly.

Step 6

Meanwhile, bring a large pot of water to a boil and season generously with salt. Add the cavatappi and cook to firm (typically 1 to 2 minutes past al dente) according to the package directions. Drain the pasta in a colander, rinse under cold water until room temperature, and transfer to the bowl with the rest of the dressing. Toss well to coat the pasta.

Step 7

Add the eggplant mixture, cherry tomatoes, mozzarella and olives and toss to combine. Add the basil and pine nuts and toss until just combined. Serve right away at room temperature or let chill in the refrigerator for the flavors to meld, covered, up to overnight. Top with more pine nuts and basil before serving if desired.