Place the asparagus in a steamer over simmering water. Steam until bright green and tender; about 5 minutes.
Fill a large frying pan about half full with water. Heat until the frying pan is full of small bubbles and just starting to simmer.
Crack the eggs into the simmering water. Cook uncovered until the whites are set but the yolks are still soft; about 3 minutes. Remove the poached eggs from the frying pan with a draining spoon and place on paper towel.
Divide the asparagus among four plates. Top each pile of asparagus with two poached eggs and a nice amount of grated cheese.
Drizzle each plate with olive oil and season with salt and pepper. Serve warm.