Bring a large pot of salted water to a boil.
Slice the asparagus into 2-inch pieces and add them to the boiling water for 1 minute then remove them and immediately rinse them under cold water. (Keep the pot of salted water at a boil.)
Reserve some of the tips of the asparagus to use as garnish. Add the rest of the asparagus to a blender, along with the toasted pine nuts, Parmesan cheese, garlic, lemon juice, salt and pepper.
Blend the ingredients for 10 to 15 seconds, then with the blender still running, slowly stream in the olive oil until it’s fully incorporated and the mixture is well-blended, scraping down the sides as needed. Transfer the pesto to a bowl and season it with salt and pepper to taste.
Add the pasta to the boiling salted water and cook until al dente. Transfer the pasta to a large serving bowl, add the pesto and reserved asparagus spears, tossing to combine. Garnish with Parmesan cheese and serve.