Step 1

Heat extra-virgin olive oil in a 12" skillet over medium-low heat. Add minced onion and cook, stirring, until soft, about 12 minutes. Add garlic and cook, stirring, for 2-4 minutes. Add crushed red pepper flakes; cook for 1 minute more. Increase heat to medium, add puréed tomatoes and season lightly with kosher salt; cook, stirring occasionally, until sauce thickens slightly and the flavors meld, about 20 minutes. Remove pan from heat, stir in basil sprigs, and set aside.

Step 2

Meanwhile, bring water to a boil in a 5-quart pot. Season with salt; add spaghetti or bucatini and cook, stirring occasionally, until about 2 minutes before tender. Drain pasta, reserving 1/2 cup pasta cooking water.

Step 3

Discard basil and heat skillet over high heat. Stir in reserved pasta water to loosen sauce; bring to a boil. Add pasta and cook, stirring, until sauce coats pasta and pasta is al dente, about 2 minutes. Remove pan from heat; add butter and cheese; toss until cheese melts. Transfer to warm bowls; serve with more cheese, if desired.