part 1
heat oil in a large skillet over medium. add shallot and garlic and cook, stirring occasionally, until softened, about 5 minutes.
add tomato paste and cook, stirring occasionally, until paste is brick red and starts to caramelize, about 5 minutes.
add vodka and cook, stirring constantly, until liquid is mostly evaporated, about 2 minutes.
add cream and red pepper flakes and stir until well blended. Season with salt and pepper; remove from heat.
part 2
cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente.
drain, reserving ~1 cup pasta cooking liquid. add pasta to skillet with sauce along with butter and ½ cup pasta cooking liquid. cook over medium-low heat, stirring constantly and adding more pasta cooking liquid if needed, until butter has melted and a thick, glossy sauce has formed, about 2 minutes.
season with salt and pepper and add 1 oz. Parmesan, tossing to coat. divide pasta among bowls, then top with basil and more Parmesan.