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Heat olive oil in a large skillet over medium low heat.
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Add onion and cook until soft and translucent, stirring occasionally, about 6-7 minutes.
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Add garlic and crushed red pepper flakes, and cook another minute.
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Increase heat to medium, and add pureed tomatoes. Season lightly with salt.
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Cook, stirring occasionally, until sauce thickens slightly and the flavors meld, about 20 minutes.
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Remove pan from heat and stir in basil sprigs.
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Meanwhile, cook spaghetti until about 2 minutes before tender (if the box says al dente takes 7 minutes to cook, then cook the pasta only 5 minutes).
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Reserve 1 cup of pasta cooking water. Drain pasta.
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Discard basil from tomato sauce and heat skillet over medium heat. Stir in 1/2 cup reserved pasta water to loosen sauce; bring to a boil.
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Add pasta and cook, stirring, until sauce coats pasta and pasta is al dente, about 2 minutes. Add more pasta water if sauce seems too thick.
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Remove pan from heat; add Parmesan cheese and toss.