Bring a pot of salted water to a boil. Meanwhile, place a colander in a large bowl of water, and then add ice. Working in 2 batches, blanch the basil in the boiling water for 20 to 30 seconds. Immediately transfser blanched basil to the ice bath.
Set aside ½ cup of the hot water and reserve the pot containing the blanching water.
Lift colander from ice water and squeeze out the excess water from the basil; transfer to paper towels and pat dry.
Add the pasta to the boiling water, and cook until al dente.
Meanwhile, pulse blanched basil, ½ cup Parmesan, pine nuts, garlic, ½ tsp salt, and ¼ tsp black pepper in a food processor until well combined. Adding a couple of tablespoons of water and pulse for another 5 to 10 seconds.
Transfer basil mixture to a medium bowl and stir in ½ cup extra-virgin olive oil.
Spoon ½ cup pesto and ¼ cup pasta cooking liquid into a large bowl. Transfer cooked pasta to the bowl and use wooden spoons or tongs to toss, adding the remaining pesto and another tbsp of cheese, until pasta is nicely coated.
Divide among bowls and top with cheese and a drizzle of oil.