Prepare the pasta according to package directions. Reserve 1/2 cup pasta water.
Heat a large saute pan. Place the Pistachio Pesto, 1/4 cup reserved pasta water (more if needed) and olive oil in the pan. Toss to incorporate. Add the cooked pasta to the pan, gently fold into the Pistachio Pesto mixture, season with salt and pepper and divide among serving plates. Garnish with the Parmesan ribbons, cherry tomatoes, basil leaves and sprinkle with pepper.
In batches, place the basil leaves, oil, pistachios, Parmesan and garlic in a blender and puree until smooth. Season with salt and pepper. Place the Pistachio Pesto in a container. Cover the top with the remaining 1 tablespoon olive oil.