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, the oregano and 1 cup of water. Increase the heat to medium-high and bring to a simmer. Reduce the heat slightly and simmer rapidly, uncovered, until thickened, 15 to 20 minutes. Season with salt and pepper.
Meanwhile, heat the remaining 3 tablespoons oil in a large nonstick skillet over medium-high heat. Add the eggplant and 1/2 teaspoon salt and cook, stirring occasionally, until golden brown and tender, 6 to 8 minutes. Transfer to a large bowl with a slotted spoon. Add the pepperoni to the pan and cook until just starting to crisp, about 2 minutes. Transfer to the bowl with the eggplant.
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.
Add the tomato sauce, parsley, half of the Asiago and half of the Parmesan to the bowl and stir well to combine. Transfer the pasta to a 3- to 4-quart baking dish and dollop the top with the ricotta, then top with the remaining Asiago and Parmesan. Bake, uncovered, until browned, about 15 minutes. Let the pasta stand about 10 minutes before serving.
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