Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Cook the diced eggplant in the hot oil, stirring frequently, until lightly browned, about 10 minutes. Stir in the red pepper and garlic; season with salt and pepper. Reduce heat to medium-low, cover, and cook until the vegetables are tender, about 20 minutes.
Meanwhile, heat 1 tablespoon of olive oil in a saucepan over medium-high heat. Stir in the chopped tomatoes, and bring to a simmer; season with fresh thyme, salt, and pepper. Reduce heat to medium-low and simmer until the tomatoes have reduced slightly, about 15 minutes.
bring a large pot of lightly-salted water to a boil; stir in the rigatoni and cook uncovered, stirring occasionally, until tender but still firm to the bite, about 13 minutes. Drain and return to the pot.
Stir the eggplant mixture into the pasta along with the basil and olives. Spoon the tomato sauce overtop to serve.