Step 1

Heat ½ cup oil in a large heavy pot over low. Add garlic and cook, stirring often with a wooden spoon, until softened but not browned, about 2 minutes.

Step 2

Increase heat to medium and add tomatoes, basil sprigs, red pepper flakes, and 1½ tsp. salt. Cook, stirring to coat, until some of the tomatoes begin to burst and release their juices, about 4 minutes. Smash some but not all of the tomatoes with the spoon to help release their liquid, then continue to cook, stirring occasionally, until a chunky, thickened sauce forms (about half the tomatoes should still be intact), 10–12 minutes. Taste and add sugar if sauce is too tart and add more salt if needed. Pluck out and discard basil sprigs.

Step 3

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente.

Step 4

Drain pasta, add to pot with sauce, and cook, stirring, until coated, about 1 minute. Remove from heat and stir in 1 oz. Parmesan.

Step 5

Divide pasta among bowls; drizzle with oil. Top with more Parmesan and 1 cup basil leaves.