Bring a large pot of generously salted water to a boil. Cook pasta according to package directions, reserving ½ cup of pasta water. Drain the pasta and return it to pot.

Heat a large skillet over medium. Add pancetta; cook, stirring occasionally until the fat has rendered and pancetta is crispy 8 to 9 minutes.

Add oil and garlic to skillet; cook over medium, stirring occasionally, until softened slightly and fragrant, about 1 minute. Add tomatoes and salt; increase heat to medium-high and cook, stirring often, until some tomatoes have burst and tomato skins soften about 4 minutes. Reduce heat to low. Using a wooden spoon, lightly break and mash about a third of the tomatoes to release their juices further.

Add tomato mixture, cheese, and ¼ cup reserved pasta water to the pot with pasta. Cook over medium-low, stirring constantly, until sauce clings to noodles, 1 to 2 minutes, adding more pasta water if needed. Remove from heat. Add basil and stir to combine. Serve with more basil and cheese.