Bring a large pot of salted water to a boil and cook the paccheri to al dente (it may take much longer than the package indicates). Reserve about ½ cup of the starchy pasta water, then drain the pasta.

Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic and cook for about 1 minute until fragrant and starting to soften but not browned. Add the tomatoes, season with salt and pepper, and stir to combine.

Cover the skillet, reduce the heat to medium-low, and simmer for about 10 minutes, stirring occasionally. When the tomatoes start to burst, smash about half of them with the back of a wooden spoon and continue to cook for another 5 minutes, covered, or until the tomatoes create a thick, silky sauce.

Uncover the skillet and continue to simmer the sauce for a few more minutes. Taste and adjust the seasoning with more salt and pepper if needed. If you want to remove some of the loose tomato skins from the sauce, you can do that at this time.

Add the drained pasta and basil along with a splash or two of the pasta water (add as much as seems necessary), and stir, cooking for a couple more minutes to allow the sauce to cling to the pasta.

Remove the pasta from the heat and stir in the cubed mozzarella cheese, allowing the residual heat of the pasta to soften it. Serve immediately with more basil on top.