Prepare the pasta water: Fill a large pot with water, add a generous pinch of salt, and bring to a rolling boil. Add the pasta and cook until al dente according to package instructions, usually 8-10 minutes.
Create the flavor base: While the pasta cooks, heat olive oil in a large skillet over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Add the minced garlic and cook for another 30 seconds until fragrant.
Develop the tomato flavor: Add tomato paste to the skillet and cook for 2-3 minutes, stirring frequently until it darkens slightly and begins to caramelize. This concentrates the flavors and reduces acidity.
Add the vodka and spice: Pour in the vodka and stir to deglaze the pan, scraping up any browned bits from the bottom. Add red pepper flakes and let the mixture simmer for 1-2 minutes until the alcohol cooks off.
Create the creamy sauce: Reduce heat to medium-low and add the heavy cream, stirring constantly until the sauce turns a beautiful orange-pink color. Allow it to simmer gently for 2 minutes to thicken slightly.
Finish with richness: Add the butter and stir until completely melted and incorporated. The butter gives the sauce a silky, glossy finish.
Reserve pasta water and drain: Before draining the pasta, reserve about ½ cup of the starchy cooking water. Drain the pasta.
Combine pasta and sauce: Add the drained pasta directly to the sauce, along with 2-3 tablespoons of the reserved pasta water. Toss thoroughly to coat each piece of pasta.
Add cheese and season: Sprinkle in the Parmesan cheese and toss until melted. Taste and adjust seasoning with salt and black pepper as needed.
Serve immediately: Transfer to warm bowls, garnish with torn basil leaves and additional Parmesan cheese if desired.