Step 1: Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente.
Step 2: While the pasta is cooking, place the toasted pine nuts, garlic cloves, and salt in a food processor. Pulse until finely minced.
Step 3: Add the fresh basil leaves to the food processor. Pulse several times until the basil is coarsely chopped.
Step 4: With the motor running on low, slowly drizzle in the extra virgin olive oil in a steady stream until the mixture is smooth and emulsified.
Step 5: Transfer the mixture to a large mixing bowl and stir in the grated Parmigiano-Reggiano and Pecorino Romano cheeses by hand. Season with black pepper.
Step 6: Before draining the pasta, reserve 1 cup of the starchy pasta water. Drain the pasta well.
Step 7: Add the hot pasta to the bowl with the pesto. Toss vigorously, adding the reserved pasta water a tablespoon at a time until the sauce reaches your desired creamy consistency.
Step 8: Serve immediately with an extra sprinkle of cheese and a few fresh basil leaves for garnish.