Cook the rigatoni according to the package directions. Drain.
Meanwhile, heat the oil in a large nonstick skillet over medium-high heat.
Add the eggplant, season with salt and pepper, and cook, stirring occasionally, until golden brown, about 8 minutes.
Add the garlic and tomatoes and cook, stirring occasionally, until the tomatoes begin to soften, 3 to 4 minutes.
Add the drained rigatoni and mint and toss. Divide among bowls and top with the ricotta salata or Parmesan.