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heat oven to 375 degrees.
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cook rigatoni according to package instructions but keep it slightly more al dente.
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reserve 1 1/2 cups pasta cooking water.
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heat 2 tablespoons olive oil in a large, oven-proof skillet over medium.
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add the eggplant, season with salt and pepper, and cook, stirring, until golden brown on all sides, 9 to 10 minutes.
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add the remaining 2 tablespoons olive oil in the skillet over medium.
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add onion and garlic and cook, stirring, until translucent, 3 to 4 minutes.
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stir in red-pepper flakes and season with salt and pepper.
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add tomatoes and their juices, crushing the tomatoes with your hands as you add them.
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cook until the tomatoes are very soft, about 5 minutes. stir in the reserved pasta cooking water, adding up to 1 1/2 cups as needed to create a silky sauce.
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drain the pasta and add it to the eggplant mixture with parmesan, 1 cup mozzarella and 1 cup basil and toss to coat.
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top with remaining 3 cups mozzarella and bake until the sauce is bubbling on the sides and the cheese is melted, about 20 minutes.