Cook the pasta according to package instructions in a large pot of salted boiling water. Drain the pasta and reserve 1/4 cup of the pasta water. Set aside.
In a large skillet, heat the olive oil over medium heat. Once the oil is hot, add the shallots and cook for 2 minutes, stirring frequently. Add minced garlic, and sauté until fragrant, about 30 seconds.
Add the tomato paste to the skillet and stir until the tomato paste is fully incorporated. Cook for 3 to 4 minutes, whisking occasionally.
Whisk in the vodka and cook for another 1 minute.
Pour in the heavy cream and the reserved pasta water, and stir until well combined.
Add the red pepper flakes, salt, and pepper to taste. Let the sauce simmer for 5 to 7 minutes, until it has thickened.
Add butter and parmesan cheese to the skillet, and whisk until the butter has melted and the sauce is well combined.
Finally, add in the cooked pasta and toss and stir until the pasta is coated evenly.
Sprinkle the parmesan cheese over the pasta and toss again until the cheese is melted and the pasta is coated in a creamy sauce.
Serve hot, topped with chopped fresh basil, shaved parmesan, and additional red pepper flakes if desired.