Bring 3 quarts of water and 2 tablespoons of salt to a boil. Drop spaghetti into boiling water; stir. Cook until al dente, about 10 to 12 minutes.
Strain tomatoes through a food mill; discard seeds and set aside.
Place a 12-inch saute pan over medium heat; add oil. Add garlic to pan. Cook, stirring occasionally, until garlic is lightly golden, about 30 seconds. Add red pepper flakes and remaining salt. Cook until garlic is medium golden, about 1 minute more.
Increase heat to high; add the strained tomatoes. Cook, swirling pan occasionally, until tomatoes start to thicken, about 5 to 6 minutes. Drain pasta in a colander, reserving some water in case sauce gets too dry. Add pasta to saute pan; toss until sauce begins to coat pasta, 3 to 4 minutes. Stir in basil; cook for 30 seconds more. Divide among bowls; sprinkle with cheese if desired.
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