Heat a medium saucepan over medium heat, add the olive oil and heat through, then add the butter and allow to melt.
Add the onion and sauté until soft and translucent, about 6 minutes. Add the garlic and sauté until just fragrant, about an additional 30 seconds.
Add the tomato paste and stir to combine, letting the paste cook for about 2 minutes, until deep red.
Add the vodka and stir to combine, then let reduce by half before stirring in the cream. Season to taste with salt and pepper then add the red pepper flakes.
Bring a large pot of water to the boil; add the salt and bring back to the boil. Pour in the pasta and cook, stirring occasionally, until al dente, about 10 minutes.
Drain, reserving 1 cup of the cooking water. Return the pasta to the pot. Ladle the sauce over the pasta and stir to combine. Stir in some of the pasta cooking water as needed.
Ladle the pasta into warmed pasta bowls and top with basil and Parmesan cheese.