Meanwhile, heat the oil in a wide, heavy skillet on medium.
Add the onion, garlic, and chile pepper to the skillet and saute until the onion is translucent, about 5 to 6 minutes.
Add the vodka and cook for 1 to 2 minutes while the alcohol evaporates.
Add the tomato puree and salt and bring the mixture to a gentle boil, then immediately lower the heat to a low simmer and let cook for about 10 minutes until reduced.
Add the rigatoni to the boiling water 2 minutes after you add the tomatoes to the skillet and cook until al dente. The pasta should take about 12 minutes to cook, but follow the package directions and adjust when to add the pasta so the sauce and pasta finish at the same time.
Stir the cream into the tomato sauce and cook for about 5 more minutes. Taste and adjust for salt if desired.
When the pasta is almost finished cooking, scoop out about ¼ cup of the cooking water and set aside.
Drain the pasta, add it to the skillet, and stir to evenly coat it in the sauce. Add some of the cooking water to make it creamier if needed. Remove from the heat.
Tear the basil and add it to the sauce, stirring lightly to mix.
Serve immediately with grated Parmesan and additional basil leaves for garnish, if desired.