Trim the ends of asparagus. Working one piece at a time, lay asparagus flat on a cutting board and shave from the end of the stalk to the leaf part using a vegetable peeler. When asparagus gets too thin to shave, chop. Place asparagus in a large bowl.**
Add arugula to shaved asparagus. Add lemon zest, lemon juice, and pesto to salad. Toss to coat.
Sprinkle with salt and pepper and top with shaved Parmesan cheese.
Serve immediately.
Notes
If you want to cook the asparagus instead of eating it raw, saute the ribbons in a tablespoon of olive oil until crisp-tender, about 2-3 minutes, and then add to bowl.