Bring a pot of water to a boil. Add the salt and then add the pasta. Cook according to package directions. Before draining the pasta, reserve 1 cup of the pasta water.
Meanwhile, heat a skillet over medium heat. Add a drizzle of oil and add the tomatoes. Saute until the tomatoes start to blister. Set aside.
Drain the pasta (after reserving some pasta water), and return the pasta to the pot. Add the pesto and toss to coat the pasta with the pesto. Add ½ cup of the pasta water and toss the pasta to create a sauce. Add additional pasta water if necessary to help the sauce come together.
Serve and garnish with the tomatoes, shaved parmesan, and fresh basil.