In a pot of salted boiling water, blanch asparagus until bright green and tender, about 2 minutes. Transfer to an ice bath and drain.
Heat a large skillet over medium-low heat. Add oil and swirl to coat. Whisk eggs in a bowl and add salt. Season with pepper. Pour into pan and cook until omelet is just set, 7 to 8 minutes. (Occasionally tilt pan and lift up sides of set egg with a spatula to allow uncooked egg to run underneath.)
Top half of omelet with Pecorino, asparagus, and arugula. Flip other half over top and cook until cheese melts, about 30 seconds more. Cut into wedges to serve.
Slice this omelet into wedges to more easily feed a crowd.