2. Pit and quarter the olives.
3. Cut the basil leaves into very thin strips.
4. Drop the rigatoni into a large pot of boiling salted water.
5. Heat the olive oil in a large non-stick sauté pan (or two pans if you don't have a very large one that will hold all of the eggplants in one batch). Fry the eggplant pieces quickly so that they brown but don't steam. Turn them once. Add the garlic, olives, most of the basil and tomato sauce. Heat the sauce and season it with salt and pepper. Keep the sauce warm.
6. When the pasta is al dente, drain it and toss with the eggplant sauce. Sprinkle with a little more basil and some grated Parmesan or pecorino cheese. Serve immediately.