Heat 3 tablespoons oil in a large skillet over mediumheat.
Add tomatoes, garlic, and red pepperflakes, season with salt, and cook, coveredslightly and swirling pan often, until tomatoesblister and burst, 10-12 minutes. Press down ontomatoes to release their juices.
Remove panfrom heat and set aside.
Meanwhile, bring 3 quarts water to a boilin a 5 quart pot. Season with salt; add pasta andcook, stirring occasionally, until about 2minutes before tender.
Drain pasta, reserving1 cup pasta cooking water.
Transfer pasta to skillet with tomatoes; setover high heat.
Add 1/2 cup pasta water. Cook,stirring and tossing often, until sauce thickensand begins to coat the pasta, about 1 minute.Stir in remaining oil, cheese, and half the basiland toss until sauce coats pasta and pastais al dente. (
Add more pasta water if sauceseems dry.)
Add remaining basil, season withsalt, and serve with breadcrumbs, if desired.