In a large heavy pot, heat 1/2 cup of oil over low heat. Add the smashed garlic and cook while stirring often with a wooden spoon, until softened, but not browned, for about 2 minutes.

Increase the heat to medium, and then add the cherry tomatoes, basil sprigs, red pepper flakes, and 1 1/2 teaspoons of salt. Stir to coat and cook until some of the tomatoes begin to burst and release their juices, which takes about 4 minutes. Use the spoon to smash some, but not all of the tomatoes to help release their liquid.

Continue to cook while stirring occasionally until a chunky, thickened sauce forms. About half of the tomatoes should still be intact. This process takes about 10-12 minutes. Taste the sauce and add sugar if it is too tart and more salt if needed. Remove and discard the basil sprigs.

While the sauce is cooking, cook the pasta in a large pot of boiling salted water. Stir occasionally until the pasta is al dente.

Drain the pasta and add it to the pot with the sauce. Cook while stirring for about 1 minute until the pasta is coated. Remove the pot from the heat and stir in 1 ounce of Parmesan.

Divide the pasta among bowls, drizzle with oil, and top with more Parmesan and 1 cup of basil leaves.