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Preheat the oven to 375°F. Butter a 9- by 13-inch ovenproof baking dish. In a large pot of salted boiling water, cook the rigatoni until al dente, about 8 minutes. Drain, then transfer to a large bowl. Toss the pasta with 2 tablespoons of the olive oil.
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Meanwhile, in a large nonstick skillet, heat 1/4 cup of the olive oil. Add half of the eggplant and season with salt and pepper. Cook over moderately high heat, stirring occasionally, until golden brown, about 5 minutes. Add the eggplant to the pasta. Repeat with another 1/4 cup of olive oil and the remaining eggplant.
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Add the onion, garlic and remaining 2 tablespoons of olive oil to the skillet. Cook over moderate heat, stirring occasionally, until the onion is lightly golden, about 5 minutes. Add the tomatoes and cook, stirring occasionally, until they have broken down and thickened to a sauce consistency, 7 to 8 minutes. Stir in the 4 tablespoons of butter.
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Add the tomato sauce to the pasta and eggplant along with the pesto and ricotta; season with salt and pepper and toss well. Transfer the rigatoni to the prepared baking dish. Top with the mozzarella and Parmigiano-Reggiano and bake for about 20 minutes, until bubbling and golden on top. Let the pasta stand for 10 minutes before serving