Preheat the oven to 400 degrees. Coat a muffin tin WELL with cooking spray.
Place the thawed shredded hash browns on a plate. Season with paprika, garlic powder, sea salt, and freshly cracked pepper, to taste. Toss to coat evenly. Spoon about 2 tablespoons of the potato mixture into each muffin cup, being sure to line the bottom and the sides very compactly. The potatoes will shrink when baking so make sure to go all the way to the top of the muffin tin when lining the sides. Bake for 15-20 minutes, and until the outer sides appear lightly golden brown and crisp. Remove from oven.
Decrease oven to 350 degrees. In the center of each hash brown nest, add a little bit of ham and grated cheese, then top with one cracked egg. Place back into the oven and bake for an additional 13-15 minutes, or until whites are set, but yolks are still soft.
Allow to cool in the pan for 2 minutes then using a butter knife, run it around the edges of each nest and gently remove it. Serve with hot sauce, sea salt, and freshly ground pepper on the side. Serve immediately.