Bring a large pot of salted water to a boil and cook the rigatoni according to package instructions until al dente.
While the pasta is cooking, heat a large skillet over medium-high heat.
Add the olive oil to the skillet and heat until shimmering.
Add the eggplant to the skillet and cook until tender and lightly browned, about 10-15 minutes.
Add the garlic to the skillet and cook until fragrant, about 1 minute.
Add the canned tomatoes and their juices to the skillet and bring to a simmer.
Let the sauce simmer for 10-15 minutes until thickened slightly.
Reserve some of the pasta cooking water and drain the rigatoni.
Add the cooked rigatoni to the skillet with the sauce and toss to combine.
If the sauce seems too thick, add a few tablespoons of the reserved pasta cooking water to the skillet to loosen it up.
Add the chopped basil to the skillet and season with salt and pepper to taste.
Serve the rigatoni with eggplant hot, garnished with grated Parmesan cheese, if desired.