Snap off the woody ends of the asparagus stalks. Use a vegetable peeler to shave the asparagus into thin wide ribbons. (The last strip of asparagus will be a little thicker than the others but it¿s fine to use.)
Pulse the basil, parsley, pine nuts, capers, garlic, 1/2 teaspoon salt and a few grinds of pepper in a food processor until coarsely ground. With the machine running, drizzle in 1/4 cup olive oil and process until the pesto is mostly smooth.
Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the asparagus noodles, red pepper flakes and a pinch each of salt and pepper. Cook, stirring, until the asparagus is tender, 3 to 5 minutes.
Add the arugula and cook until just wilted, about 1 minute. Remove from the heat; add the pesto and 1 tablespoon water and toss to coat. Stir in the lemon zest and season with salt. Top with more zest.