Cut woodsy ends of asparagus off and discard. Chopped asparagus into 2 inch pieces.
Blanch asparagus: Bring pot of water to a boil, cook asparagus 5-6 minutes until tender. Strain asparagus and add to bowl of ice water to stop cooking. Let sit in ice bath for 1-2 minutes and then drain.
Toast pine nuts: In a dry skillet, cook pine nuts over medium heat for no more than 3 minutes. Stir frequently to prevent scorching. Remove from skillet.
In food processor, blend together the cooked asparagus, toasted pine nuts, garlic, olive oil, lemon zest, lemon juice, dash of salt, and dash of pepper until pureed.
If desired, add parmesan cheese and blend for one more minute. You may need to add another tablespoon of olive oil if mixture is too thick for your preference.
Use pesto immediately or store in an airtight container in the refrigerator.