In a 10- or 11-inch sauté pan, heat the oil and garlic over medium-low heat, stirring occasionally, until the garlic is softened but not browned, about 5 minutes. Add the tomatoes, salt, and pepper to taste. Toss gently to coat and then raise the heat to medium. Simmer, stirring occasionally and adjusting the heat to maintain a lively but not too vigorous simmer, until the tomatoes have been reduced to a thick, pulpy sauce, 15 to 20 minutes. Remove from the heat. Sprinkle on the basil and stir to combine thoroughly.
While the sauce is cooking, bring a large pot of abundantly salted water to a vigorous boil and cook the pasta until al dente. Drain it well. Taste the sauce and adjust the seasonings if needed. Toss the pasta with three-quarters of the sauce and divide among individual serving bowls. Spoon a little of the remaining sauce over each serving and sprinkle on the cheese, if you like.