Cook pasta in salted water
Drain pasta, saving 2 cups of pasta water in a bowl. Set the pasta aside in a separate bowl
In the empty pot, heat olive oil and butter over medium heat. Add shallots, garlic, and red pepper flakes. Cook for 3 minutes.
Pour in the vodka and cook until is evaporates
Add the tomato paste and cook for 3 minutes
Add 1 cup of the reserved pasta water and stir until the mixture is saucy.
Add a few grinds of salt and black pepper and let simmer for 2 minutes
Add the cream and mix in
Finally, combine the pasta and the sauce and coat it evenly. Add splashes of pasta water if needed to loosen the sauce
Scoop into bowls and top with basil and your choice of cheese