Preheat the oven to 450 degrees F. Bring a large pot of salted water to a boil.
Heat 2 tablespoons of the oil in a medium saucepan over medium heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic is golden, about 2 minutes. Add both cans of tomatoes and 1 cup water. Increase the heat to medium-high and bring to a simmer. Reduce the heat slightly, add the basil and simmer rapidly, uncovered, until thickened, 15 to 20 minutes. Discard the basil and season with salt and pepper.
Meanwhile, heat the remaining 2 tablespoons oil in a large skillet over medium heat. Add the pancetta and cook, stirring occasionally, until browned and crispy, about 8 minutes. Transfer to a large bowl using a slotted spoon. Increase the heat to medium-high, add the eggplant to the pancetta drippings and cook, stirring occasionally, until golden brown and tender, 6 to 8 minutes. Transfer to the bowl with the pancetta.
Cook the cavatappi in the salted boiling water until very al dente, about 2 minutes less than the package directions. Drain the pasta and add it to the bowl with the pancetta and eggplant.
Add the tomato sauce, half of the mozzarella and half of the Parmesan to the bowl and stir well to combine. Transfer the pasta mixture to a 3- to 4-quart baking dish and top with the remaining mozzarella and Parmesan. Bake, uncovered, until browned, about 15 minutes. Let the pasta stand about 10 minutes before serving.
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