Bring a large pot of salted water to a boil. Meanwhile, in cold water, gently wash basil. Drain and gently but thoroughly dry basil with paper towels. Put about ¼ of the basil in a mortar. Using the pestle with a rotary movement, grind basil against wall of mortar until mostly ground, then, in batches, repeat with remaining basil until all leaves are ground. 

 

Working with 1 tablespoon at a time, add and grind pine nuts, then add garlic and a generous pinch salt; grind until garlic is ground. Working with 1 to 2 tablespoons at a time, add and grind cheeses. Working with 1 to 2 tablespoons at a time, drizzle in oil, grinding and mixing to incorporate as you go, until pesto is combined and smooth. 

 

Cook pasta in the boiling water until al dente. Reserving 1/3 cup pasta cooking liquid, drain pasta. Return pasta to pot and immediately add pesto and 3 tablespoons pasta cooking liquid; toss to combine. Moisten with more pasta cooking liquid, if desired. Divide among serving bowls and season with pepper. Serve immediately