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1
For the sauce: Heat 3 tablespoons of the oil in a wide saucepan over medium-high heat. Once the oil shimmers, carefully add the tomatoes and salt. Cook for 2 or 3 minutes, stirring, until the tomatoes soften, then reduce the heat to medium; use a potato masher to break down the tomatoes and form a sauce. Add the reserved tomato juices to thin the sauce as needed. Cook for 20 minutes, stirring occasionally. Remove from the heat.
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2
Meanwhile, heat the remaining 1/2 cup of oil in a small saucepan over medium heat. Add the garlic, basil and crushed red pepper flakes. Stir until the basil wilts and the garlic turns light brown, about 5 minutes. Remove from the heat; steep for 5 minutes, then strain through a fine-mesh strainer; discard the solids. Add half of the oil to the tomato sauce. Taste, and add salt as needed.
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3
For assembly: Bring a large pot of water to a boil over medium-high heat. Add a generous pinch of salt.
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4
Meanwhile, warm the sauce in a large saute pan over medium heat.
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5
Add the pasta to the boiling water; cook until it is just shy of tender, about 2 minutes. Drain, reserving at least 1/4 cup of the cooking water. Add the pasta and 1/4 cup of the pasta water to the pan with the tomato sauce; increase the heat to medium-high, shaking the pan to incorporate the sauce and the pasta. Cook for 2 to 3 minutes.
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6
Remove from the heat. Stir in the cheese, butter and basil, tossing gently to incorporate. Divide the pasta among individual wide, shallow bowls. Drizzle with oil, if desired; serve warm.
