1 teaspoon finely grated lemon zest, plus more for topping
The asparagus stalks' woody ends should be cut off. To create thin, wide ribbons out of the asparagus, use a vegetable peeler. (The final asparagus strip will be slightly thicker than the others, but you may still use it.)
Use a food processor to coarsely mince the basil, parsley, pine nuts, capers, garlic, 1/2 teaspoon salt, and a few grinds of pepper. Add 1/4 cup olive oil while the machine is running and continue processing until the pesto is largely smooth.
In a big nonstick skillet, heat the last tablespoon of olive oil over medium-high heat. Add a dash of each salt and pepper, the asparagus noodles, and the red pepper flakes. For 3 to 5 minutes, cook the asparagus while stirring.
Arugula should just be lightly wilted, which takes approximately a minute. Remove from the heat, then stir in 1 tablespoon water and the pesto before serving. Add the lemon zest and salt after stirring. Put extra zest on top.