Fill a pot with 2 inches of water and insert a steamer basket. Bring water to a boil. Add asparagus and steam until tender,2 to 6 minutes.
Fill a large saucepan with 4 inches of water and bring to a boil.Reduce heat to medium.When water is barely simmering,break 1 egg into a small heatproof bowl.
Gently tip bowl,sliding the egg carefully into water.Repeat with remaining eggs.Cook until whites are set but yolks are soft,2 to 3 minutes.
Using a slotted spoon,transfer eggs to paper towels,drain briefly.
Divide asparagus among 4 plates,and top each with an egg.Drizzle with oil,sprinkle with Parmesan,and season with salt and pepper.
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