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