Mix the grated potatoes, olive oil, salt, and pepper in a medium sized mixing bowl.
Grease the ramekins and divide the hash brown mixture evenly in each one, spooning out a small hole in the middle like a nest for an egg to sit in.
Bake at 425 for 15 minutes or until the edges are browned.
Remove from oven and crack an egg in each cup. Add the parsley with a pinch of salt and pepper on top. Bake at 350 for about 15 minutes or until egg whites have hardened.
Remove from oven and let cool before serving.