Bring a medium pot of generously salted water to boil for the pasta. Once boiling, add pasta and cook until al dente.
While your pasta is boiling, in a large pot, heat olive oil and butter over medium heat. Once the butter is melted, add garlic and red pepper flakes. Cook until the garlic begins to turn golden and aromatic, about 1 minutes.
Add tomato paste and cook, stirring often, until paste darkens in color and begins to caramelize on the bottom of the pan, 3 to 5 minutes.
Turn heat to low and switch to a heat resistant whisk. Carefully add the vodka (the sauce will sizzle and pop aggressively for a few seconds). Whisk, scraping any cooked-on bits from the bottom of the pan, until the vodka is incorporated into the sauce.
Whisk in heavy cream. Bring the sauce up to just barely a simmer, and let it cook, stirring frequently, for 5 minutes. Do not allow it to come to a full boil.
When the pasta is nearly done, use a heat-proof measuring cup to scoop out ¼ cup of the cooking water and whisk it into your sauce. Taste the sauce and add salt as needed.
Once the pasta is al dente, scoop out and reserve another ¼ cup of the cooking water. Drain pasta or use a spider skimmer to scoop pasta out of the water and add pasta to the sauce. Stir to combine.
The sauce will seem a little thin at first. Allow it to sit for about 5 minutes to thicken. If the sauce gets too thick, stir a bit more of the reserved pasta water into the sauce.
Serve topped with grated Parmesan and basil if desired and enjoy!