1 pound eggplant, peeled and cut into ¾-inch cubes
6 tablespoons extra-virgin olive oil, divided
12 ounces penne rigate or mezze rigatoni pasta
8 large garlic cloves, finely chopped
1/2 teaspoon red pepper flakes
2 pints grape tomatoes
2 tablespoons white balsamic vinegar
1/2 cup lightly packed fresh basil leaves, roughly chopped
2 ounces ricotta salata, shredded
Heat the oven to 475°F with a rack in the upper-middle position. Line a rimmed baking sheet with kitchen parchment. In a large bowl, toss the eggplant with 1½ teaspoons salt and 4 tablespoons of the oil. Spread in a single layer on the prepared baking sheet and roast until browned and tender, 30 to 35 minutes, stirring once.
Meanwhile, in a large pot, bring 4 quarts of water to a boil. Stir in the pasta and 2 tablespoons salt; cook until the pasta is al dente. Reserve about ½ cup of the cooking water, then drain the pasta.
While the eggplant roasts and the water heats, in a 12-inch skillet over medium-high, heat the remaining 2 tablespoons oil until shimmering. Add the garlic and pepper flakes and cook, stirring, until fragrant, about 30 seconds. Add the tomatoes and 1½ teaspoons salt, then cover and cook, occasionally shaking the pan, until the tomatoes begin to release their liquid, about 1 minute. Stir in the vinegar, then use the back of a large spoon to crush the tomatoes. Cover, reduce to medium and cook, stirring, until the mixture breaks down into a lightly thickened sauce, 8 to 9 minutes.