Place the grated potatoes in between some paper towels or a cheesecloth and wring out as much moisture as you can.
Place the potatoes on a fresh paper towel, sprinkle with salt, top with another paper towel, and let it sit for 20 minutes.
Preheat the oven to 350 degrees.
Use vegetable spray to lightly coat 4 cupcake tins. Press the grated potatoes on the bottom and sides of the tins. Sprinkle the cheese on the bottom of the tins and season with salt/pepper if desired.
Bake for 20 minutes, checking them periodically.
Once it the potatoes have firmed up a bit and have started to brown slightly, remove them from the oven. Take a butter knife and carefully work your way around the hash brown cup to loosen it up. This makes it easier to remove later.
Decrease the heat to 300 degrees.
Lightly tap the eggs on a flat surface. (Cracking an egg on an edge pushes the shell up inside, which you don’t want.) Drop the eggs into the hash brown cups and sprinkle lightly with salt and pepper. Bake for about 15 minutes, it’s done when the white part is firm.
Use a butter knife to loosen the edges around the cupcake tin. Take a fork and carefully lift up the bottom and scoop it out. Sprinkle with fresh parsley and serve!