Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.

In a food processor, combine the basil leaves, pistachios, Parmesan cheese, garlic, and lemon juice. Pulse until finely chopped.

With the food processor running, slowly drizzle in the olive oil until the mixture is smooth and creamy. If the pesto is too thick, add a little reserved pasta water until you reach your desired consistency. Season with salt and pepper to taste.

In a large mixing bowl, combine the cooked pasta and pistachio pesto. Toss until the pasta is evenly coated. If needed, add more reserved pasta water to loosen the sauce.

Serve the pasta in bowls, topped with pieces of burrata cheese and cherry tomatoes if using. Drizzle with a little extra olive oil and sprinkle with additional Parmesan cheese if desired.

Enjoy immediately, or let it cool and serve as a cold pasta salad.