Bring a large pot of water to a boil. Add a pinch of kosher salt. Add pasta and cook till al dente, about 9 minutes. (Package instructions may say up to 11 minutes but the pasta will continue cooking as its tossed with the other ingredients so it’s best to undercook it a little bit.) Drain pasta. Do not rinse.
Heat olive oil in a large skillet over high heat. Add the cherry tomatoes and cook for 30 seconds. Add pasta and pesto. Cook 1 minute, stirring to coat pasta with the pesto. Add the mozzarella. Stir to incorporate. Add the fresh basil and remove from the heat.
Divide pasta among bowls and sprinkle each with some fresh shavings of Parmigiano. Crack the pepper overtop and serve.