In a large skillet over medium heat, melt 3 tbsp butter.
Add 1 shallot and 2 cloves garlic and cook, stirring frequently, until softened, approximately 4 to 5 minutes.
Add 1/2 cup tomato paste and 1/2 tsp crushed red pepper flakes and cook, stirring frequently, until paste has coated shallots and garlic and is beginning to darken, approximately 5 minutes.
Add 1/4 cup vodka to pot and stir to incorporate, scraping up any browned bits from the bottom of the pot. Turn off heat.
Bring a large pot of salted water to a boil and cook 1 lb tubed pasta until al dente. Reserve 2 cups of pasta water before draining.
Return sauce to medium heat and add 1/4 cup of the pasta water and 1/2 cup heavy cream, stirring to combine.
Add half the Parmesan cheese and stir until melted.
Fold in remaining Parmesan cheese, adding more pasta water, about a tablespoon at a time, if the sauce is looking dry.
Season with kosher salt if needed.
Serve topped with more Parmesan cheese and tor basil leaves.
