Cook the tortellini according to package instructions. While the pasta is cooking, make an ice water bath: Dissolve the kosher salt and in the warm water in a large bowl. Add 4 cups each ice and water and reserve. Drain the pasta, cool in the ice water bath for 2 minutes, then drain again and transfer the tortelloni to a large bowl. Whisk together the pesto and the 1/4 cup cold water and toss gently with the tortellini. Add the fresh mozzarella and tomatoes and gently fold to incorporate. Top with Parmigiano Reggiano and fresh basil.