In a wide pan over medium-high heat, heat 1/3 cup of olive oil until quite hot. Add the tomatoes, red pepper flakes, and season lightly with the salt and pepper. (I always start with a light hand with the salt and pepper because as the tomatoes reduce, the salt will become concentrated.) Using a potato masher, mash the tomatoes finely. (This will be easier to do as the tomatoes begin to heat up.) Cook the tomatoes for 20 to 25 minutes, until the tomatoes are tender and the sauce has thickened.

Meanwhile, stack and roll the basil leaves into a cylinder and cut thinly crosswise into a chiffonade.

Bring a large pot of amply salted water to a boil. Cook the spaghetti until just shy of al dente. Reserve a little of the pasta cooking water. Add the pasta to the sauce and cook over medium-high heat, gently tossing the pasta and the sauce together with a couple of wooden spoons and a lot of exaggerated movement (you can even shake the pan) until the pasta is just tender and the sauce, if any oil had separated from it, now looks cohesive. (If the sauce seems too thick, add a little pasta cooking liquid to adjust it.) Take the pan off of the heat and toss the butter, basil and cheese with the pasta in the same manner (the pasta should take on an orange hue) and serve immediately.

Cook's Note: Here is a good tip for peeling and seeding tomatoes: Bring a large pot of water to a boil. Have a large bowl of ice water nearby. Cut a small shallow X on the bottom of each tomato. Ease about 5 tomatoes into the pot and cook for about 15 seconds, and then promptly move them to the ice water. (Do this with the remaining tomatoes.) Pull off the skin with the tip of a paring knife. If the skin sticks, try a vegetable peeler using a gentle sawing motion. Cut the tomatoes in half and use your finger to flick out the seeds.