Begin by draining the burrata cheese, then place it in a bowl of warm water to soften while you prepare the pasta. Let it soak for about 10 minutes.

Bring a large pot of generously salted water to a rolling boil. Add the pappardelle pasta and cook according to package instructions until al dente, typically about 8 to 10 minutes. Reserve a cup of pasta water, then drain the pasta and return it to the pot.

In a food processor, combine fresh basil leaves, shelled pistachios, grated Parmesan cheese, minced garlic, salt, and pepper. Pulse until finely chopped, then gradually pour in lemon juice and olive oil while blending until smooth.

In a small bowl, mix cornstarch with warm water until dissolved. Microwave this mixture for about 30 seconds until it thickens into a jelly-like consistency. Mix it into the prepared pesto.

Pour the pistachio pesto into the pot with the warm pappardelle. Toss gently for about 1 to 2 minutes, allowing the pasta to become thoroughly coated.

Tear pieces of the softened burrata over the top of the pasta, season with olive oil and salt. Garnish with crushed pistachios.