Preheat your oven to 400°F (204°C).
Lightly grease three small baking dishes with olive oil, using a pastry brush to coat evenly. Set them aside on a baking sheet.
In a small pot, bring water to a rolling boil. Add a pinch of salt and the chopped asparagus. Stir briefly.
Once the pot returns to a boil, remove it from heat, drain the asparagus, and immediately transfer it to a bowl of ice-cold water to halt the cooking process. Drain again thoroughly.
Divide the asparagus evenly among the three prepared baking dishes, placing it as a base layer.
Top each dish with one teaspoon of butter and sprinkle with 1/4 teaspoon of salt.
Carefully crack two eggs into each baking dish. Make sure not to break the yolks.
Bake in the preheated oven for 7 minutes.
Remove from the oven, sprinkle each dish with one tablespoon of parmesan cheese and a dash of ground black pepper.
Return to the oven and bake for an additional 7 minutes, or until the egg whites are just set but the yolks remain slightly runny.
Serve immediately as a wholesome, beautifully colorful dish!