We love the combination of smoky roasted peppers and garlicky sauteed eggplant in this pasta dish that can be served hot, warm, or at room temperature.
Place peppers directly over a gas flame and cook, turning occasionally, until charred all over, 8 to 10 minutes. Transfer to a bowl; cover with plastic wrap until cool enough to handle. Rub off charred skin with a paper towel; discard. Remove and discard seeds. Cut peppers into 1/4-inch strips.
Meanwhile, heat 1/3 cup oil in a large nonstick skillet over medium-high. Add eggplants, garlic, and 1 teaspoon salt; stir to combine. Add 1/3 cup water. Cover and cook, stirring occasionally and adding more water if needed, until eggplants are very tender but still hold shape, 10 minutes. Stir in oregano; cook 1 minute. Transfer to a large bowl; add peppers, remaining 1/3 cup oil, vinegar, parsley, and cheese. Let stand while cooking pasta.
Bring a large pot of salted water to a boil. Add pasta; cook according to package directions until al dente. Reserve 1/2 cup liquid, then drain. Toss pasta with eggplant mixture until fully coated (add pasta water if needed to moisten, 1/4 cup at a time). Season with salt and pepper, sprinkle with parsley leaves, and serve.