In large frying pan, bring 1 inch of water with a large pinch of salt to boil. Lay asparagus in pan, cover with lid and cook for 2-4 minutes (depending on thickness of spears) on medium heat until just tender. Drain and plate asparagus on serving plate.
Wipe frying pan clean. Heat the olive oil over medium heat . When hot, add egg(s) to pan and fry 2 minutes. Turn heat to low, cover pan and cook an additional 1-2 minutes until egg whites cooked through. Slide eggs on top of asparagus.
Season with salt and pepper. Shave Parmesan cheese on top with vegetable peeler.