Set a pot of water to boil for the pasta. Next prepare the sauce. In a large pan heat 1 tablespoon of olive oil, then add 1 clove of minced garlic and heat for about 20 seconds, then add the passata and basil leaves with a pinch of salt and sugar. Cook for 15 minutes over low heat.
Add salt to boiling water together with rigatoni, cook according to package instructions.
While the pasta is cooking and the sauce is simmering, slice the eggplants thickly, then heat 2 tablespoons of olive oil in a frying pan and fry the eggplant slices. You might need to fry in batches add more oil as needed. Once cooked on both sides, which will take 2-3 minutes per side, remove from the oil and put on two sheets of paper towel to absorb excess oil.
Drain the pasta and add to the sauce, toss to combine, add salt if needed. Serve the pasta topped with eggplant slices and grated Parmesan or Pecorino cheese. (Or use grated Ricotta Salata if you are able to source it.)