Cook pasta in a large pot of salted boiling water until al dente. Reserve 1 cup of pasta water before draining.
In a large pan, heat olive oil over medium heat. Add finely chopped onion and sauté until softened and translucent.
Stir in minced garlic and cook for an additional minute until fragrant.
Add tomato paste to the pan, stirring constantly for 2-3 minutes until it darkens in color and develops a richer flavor.
Pour in vodka, deglazing the pan, and let it cook for a minute to allow the alcohol to evaporate.
Lower the heat and stir in heavy cream, chili flakes, salt, and black pepper until the sauce becomes smooth and creamy.
Gradually add the reserved pasta water, a little at a time, to loosen the sauce and achieve a silky consistency.
Add the cooked pasta to the sauce, tossing to coat every piece evenly.
Stir in grated Parmesan cheese and butter until melted and fully combined.
Serve immediately, garnished with fresh basil leaves and extra Parmesan, if desired.