Bring a large pot of water to a boil. Blanche basil leaves for 20 to 30 seconds or until vibrant green. Remove from boiling water and immediately immerse in an ice water bath to halt the cooking process. Drain. Keep the pot of water boiling on the stove.
In a food processor, combine basil, olive oil, parmesan, pine nuts, pecorino, and garlic. Pulse until smooth; season with salt and pepper.
Add pasta to boiling water and cook until al dente. Drain, reserving 1/2 cup of cooking water. Return pasta to pot. Toss with pesto until evenly coated, adding reserved cooking water as needed to thin sauce. Serve immediately.
