In a pan, add 3 tablespoon olive oil, eggplant cubes, garlic cloves (not peeled) and cook until the eggplant cubes are soft and light brown. Stir occasionally.
Add the cherry tomatoes (or tomato cut into cubes) and cook just 2-3 minutes. Add balsamic vinegar, cane sugar, and mix well so everything is well-coated. Cook 2-3 minutes.
Remove all the garlic cloves from the pan and peel them.
In a food processor, put the eggplant mixture, the peeled garlic, basil leaves, a pinch of coarse sea salt and pepper. Pulse until almost pureed. Add olive oil (2-3 tablespoon) and pulse again until the olive oil is incorporated.
Meanwhile, bring a large saucepan of salted water to a boil. Add Rigatoni Pasta and cook for about 12 minutes or until al dente, stirring from time to time. Drain and put them in a serving bowl.
Add the Roasted Eggplant sauce and mix well.
Serve in a plate with some parmesan shavings.