8 ounces dry
linguine or spaghetti
2 tablespoons olive oil
4 cloves garlic, thinly sliced
1 small eggplant (about 1 pound), cut into 1-inch cubes
2 medium zucchini or summer squash, halved and sliced into 1/4-inch-thick slices
1 teaspoon kosher salt, divided
1/4 teaspoon freshly ground black pepper
2 cups chopped plum tomatoes or halved cherry tomatoes
Kernels from 1 ear corn
2 medium carrots, peeled and shaved into ribbons
1/2 cup dry white wine
2 tablespoons unsalted butter
1/2 cup shredded Parmesan cheese, plus more for garnish
1/4 cup torn fresh basil leaves
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, 7 to 9 minutes, or according to package instructions. Reserve 1/2 cup of the cooking water, drain the pasta, and set it aside.
Meanwhile, heat the oil in a large, high-sided skillet over medium heat until shimmering. Add the garlic. Cook, stirring frequently, until golden, about 2 minutes. Use a slotted spoon to transfer the garlic to a paper towel-lined plate.
Add the eggplant, zucchini, 1/2 teaspoon of the salt, and pepper and cook, stirring occasionally, until the vegetables start to soften, about 3 minutes. Stir in the tomatoes and cook for 5 minutes. Stir in the corn, carrots, remaining 1/4 teaspoon salt, and reserved garlic. Cook 1 minute more.
Add the wine and simmer until reduced by about half, 1 to 2 minutes. Add the reserved pasta water and butter, and bring to a boil. Add the pasta, then toss to coat with the sauce. Remove from the heat and stir in the cheese and basil.
Divide among bowls or plates, top with additional cheese if desired, and serve warm.