Heat the broiler. In a small bowl, whisk together 2 tablespoons of the oil, the vinegar, 1 teaspoon salt, and a few grinds of pepper.
Brush the mixture on the cut sides of the zucchini, eggplant, and onion. Arrange them cut-side up in a large, shallow baking pan.
Broil the vegetables until golden brown and tender, 6 to 8 minutes per side. Transfer to a cutting board. Cut the zucchini crosswise into thin slices. Cut the eggplant into 1-inch pieces. Chop the onion coarsely.
Meanwhile, in a large pot, cook the pasta according to the package directions; drain.
Return the pot to the stove, add the garlic and the remaining oil, and cook over low heat until the garlic sizzles. Stir in the oregano and mint.
Add the cooked pasta, broiled vegetables, tomatoes, Feta, ½ teaspoon salt, and a few more grinds of pepper. Warm over low heat if necessary. Sprinkle with the Parmesan before serving.
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