This is our simplest, best version of spaghetti and red sauce. Two types of tomatoes can be used with our basic method: ripe cherry tomatoes or canned Italian plum tomatoes.
Cover and bring 3 quarts of salted water to a boil in a large stockpot.
If using cherry tomatoes, wash and stem. If using vine-ripened tomatoes, prepare an ice-water bath; bring a large pot of water to a boil. Using a paring knife, score nonstem end of each tomato with a shallow x. Blanch tomatoes in boiling water for 30 seconds. With a slotted spoon, transfer tomatoes to ice bath (keep water simmering). Using a chefs knife, cut flesh into 1/4-inch strips; set aside. Press cores of tomatoes through a sieve; discard seeds. If using canned tomatoes, strain, and pass through a food mill fitted with a fine disk.
Drop pasta into boiling water; stir. Cook until al dente, about 11 minutes.
Meanwhile, place a 12-inch skillet over medium heat; add oil. Add garlic; cook, stirring occasionally, until garlic is lightly golden, about 30 seconds. Add red-pepper flakes and 1/4 teaspoon salt. Cook until the garlic is medium golden, about 1 minute.
Increase heat to high. Tilting pan at an angle, add tomato strips and pulp from sieve. Cook, swirling pan occasionally, until tomatoes begin to break down, cherry tomatoes begin to burst, or canned tomatoes begin to thicken, 5 to 6 minutes. If using cherry tomatoes, mash a few with a spoon (if they start to get too dry, add a little water from the pasta stockpot).
Drain pasta in a colander, reserving 1 cup cooking liquid in case the sauce gets too dry. Add pasta to sauce; cook until sauce clings to pasta, 3 to 4 minutes. Stir in basil; cook 30 seconds more. Divide among bowls; sprinkle with cheese, if using. Serve.