Bring a large pot of heavily salted water to a boil. Add the penne and cook for 9 minutes.
While the penne is cooking, make the sauce. Place 4 tablespoons olive oil in a large cold skillet. Add the chilies and garlic, turn the heat to medium-low and cook, stirring frequently, until fragrant but the garlic is not browning, about 4 minutes. Add the sauce and a pinch of salt and pepper. Let the sauce simmer until the penne is ready. Reserve some of the starchy cooking liquid from the penne and drain. Add to the sauce and let simmer for another 2 minutes adding some of the reserved cooking liquid is needed. Taste and add more salt and pepper if needed. Stir in the basil.
Serve with a drizzle of olive oil and Parmesan cheese.