Bring a large pot of salted water to a boil. Cook the rigatoni in the boiling water according to the package directions until al dente. Reserve 1 cup of the cooking water, then drain the pasta.
Meanwhile, in a very large high-sided skillet, warm ¼ cup of the olive oil over medium-high heat until it begins to shimmer.
Add ⅓ of the eggplant and a very generous pinch of salt and sauté, stirring or tossing often, until fork tender and lightly browned on all sides, about 6 minutes.
Using a slotted spoon, transfer the eggplant to a bowl; repeat twice more with the remaining oil and eggplant.
Add the tomatoes and a very generous pinch of salt and sauté until jammy, for 6 to 8 minutes.
Add the garlic, oregano and red pepper flakes and sauté an additional minute.
Add the pasta, eggplant and ¼ cup of the reserved pasta water and toss to coat, adding more pasta water, as needed, to create a velvety sauce. Season with salt, to taste.
Serve immediately with a generous dollop of ricotta cheese.