Heat olive oil in a 10-inch oven-proof frying pan over medium high heat.
Add onions and salt, stirring occasionally until onions are softened, about 3 minutes.
Add asparagus, reduce heat to medium-low, and cook, covered, until the asparagus are barely tender, 6 to 8 minutes.
Pour in eggs and cook until almost set but still runny on top, about 2 minutes.
Sprinkle cheese over and put in oven to broil until cheese is melted and browned, about 3 to 4 minutes.
Remove from oven with oven mitts and slide frittata onto a serving plate. Cut into wedges.