Bring a large pot of lightly salted water to a boil; cook the orecchiette pasta according to package instructions al dente; drain and rinse the pasta under cool water to prevent them from sticking to one another, and set aside.
To prepare the pesto sauce, place the basil, garlic, walnuts and Parmesan cheese in the food processor; season with salt and pepper, to taste, and blend.
While the food processor is on, slowly drizzle the olive oil into the mixture. Stop to scrape down the sides as necessary, and continue to mix until the pesto is well-blended and smooth.
Toss the half of the pesto sauce (or more) with the cooked orecchiette pasta. Fold in the grape tomatoes, mozzarella, and fresh basil.
Serve cold or at room temperature.