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1
Bring a large pot of salted water to a boil.
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2
Meanwhile, heat 2 Tbsp. oil in a large Dutch oven or other heavy pot over medium. Cook onion and garlic, stirring constantly, just until onion is starting to brown around the edges, 5-7 minutes. Add tomato paste and red pepper flakes and stir to coat onion. Cook, stirring often, until paste is deep red and starting to brown and stick to the bottom of pot, 5-7 minutes. Add vodka, scraping up brown bits; reduce heat to low.
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3
Using a heatproof measuring glass, scoop out about 1/4 cup boiling water from pot and add heavy cream. Stirring constantly, gradually pour cream mixture into onion mixture and cook, stirring, until a smooth sauce forms. Remove from heat.
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4
Cook pasta in the pot of boiling water, stirring occasionally, until al dente. About 1 minute before pasta is done, scoop out 1 cup pasta cooking liquid.
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5
Return Dutch oven to low heat. Using a slotted spoon, transfer pasta to Dutch oven. Stir in 1/2 cup pasta cooking liquid, then gradually add half of Parmesan, stirring constantly to melt. Pasta should be coated with a smooth, glossy sauce. Season with salt; add more pasta cooking liquid if sauce is too thick.
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6
Divide pasta among bowls. Top with basil and remaining Parmesan and drizzle with a little oil.
