Pre-heat the oven to 400°F.
Place individual baking dishes on a baking sheet; add one teaspoon of olive oil to each dish.
Use a pastry brush to spread the olive oil around the inside of the baking dishes; set aside.
Bring a small pot of water to a hard boil; add a dash of salt and the chopped asparagus; stir.
When the water returns to a boil, remove from heat.
Drain the asparagus and transfer to a large bowl of cold water; this will stop the cooking process and save the asparagus from wilting.
Drain the cold water well from the asparagus.
Distribute the asparagus among the prepared baking dishes.
Top the center of each baking dish with a teaspoon of butter.
Season with the remaining 1/2 teaspoon salt.
Crack two eggs into each baking dish, being extra careful not to break the yolks.
Place in the pre-heated oven and bake for 7 minutes.
Remove from oven and top each portion with one tablespoon of parmesan cheese and 1/4 teaspoon of ground black pepper.
Return to oven and bake for 7 more minutes.
Serve immediately.
