Heat the 1/4 cup of oil in a large pan over medium-low heat.
Add the shallot and garlic and cook, stirring occasionally, until softened (about 5 minutes). Next, add the tomato paste and cook, again stirring occasionally, until the paste is brick red and starts to caramelize (about 5 minutes).
Add vodka and cook, stirring constantly this time, until liquid is evaporated (about 2 minutes). Add cream and red pepper flakes and stir until well combined. Season with salt and pepper and remove from heat.
Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally (until al dente). Drain, but reserve 1 cup pasta cooking liquid. Add the pasta to the 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, about 2 minutes). Season with salt and pepper and add Parmesan. Stir. Divide pasta among bowls, then top with Parmesan and basil (if using).