Bring a large pot of generously salted water to a boil. Cook rigatoni until al dente. Reserve ½ cup of pasta water before draining.
In a large skillet over medium heat, warm olive oil. Add diced onion and cook 4–5 minutes until soft and translucent. Stir in garlic and cook 30 seconds until fragrant.
Add tomato paste and red pepper flakes. Stir constantly and cook for 2–3 minutes until the paste deepens in color and starts to stick slightly to the pan.
Pour in the vodka and stir, scraping up any browned bits from the bottom of the skillet. Let it bubble for 1–2 minutes until the alcohol cooks off and the mixture thickens.
Reduce heat to low. Stir in heavy cream and butter until silky smooth. If too thick, add reserved pasta water a splash at a time. Stir in grated Parmesan and season with salt and pepper.
Add drained rigatoni to the skillet. Toss gently until every piece is coated in the creamy sauce. Transfer to a serving bowl, top with extra Parmesan and fresh basil, and serve immediately.