Bring a large pot of water to a boil, generously season it with salt until it resembles the salinity of the sea, and cook the pasta until al dente following the package instructions.
In a large, deep sauté pan, melt the butter over medium-low heat.
Incorporate the red onion and season with a pinch of salt and freshly ground pepper; sauté gently for 5 to 7 minutes, stirring occasionally until the onion is soft and translucent.
Stir in the garlic and cook for approximately 1 minute, just until its aroma is released.
Mix in the tomato paste and continue to cook, stirring now and then, until it deepens in color—about 5 minutes.
Pour in the vodka, allowing it to simmer until mostly evaporated, about 1 minute.
Add the heavy cream and red pepper flakes, stirring to fully integrate. Let the sauce simmer for 2 minutes until slightly thickened.
Toss in the drained pasta along with the reserved pasta water, stirring well to coat the pasta thoroughly with the sauce.
Remove from heat, sprinkle in the grated parmesan cheese, and mix until fully melted and incorporated.
Serve immediately, topped with additional parmesan and a few fresh basil leaves for a burst of color and flavor.