Preheat the oven to 400°F (200°C).
In a large bowl, combine the shredded hash browns, salt, black pepper, and garlic powder. Mix well.
Brush a 6-cup muffin tin with melted butter to prevent sticking.
Divide the hash brown mixture evenly among the muffin cups, pressing the potatoes up the sides to form baskets with a hollow center.
Brush the tops of the hash brown baskets with the remaining melted butter.
Bake the hash brown baskets for 15 minutes until they start to turn golden and crisp.
Remove the muffin tin from the oven and carefully crack one egg into the center of each hash brown basket.
Sprinkle shredded cheddar cheese evenly over each egg.
Return the muffin tin to the oven and bake for an additional 10 minutes, or until the egg whites are set and the yolks reach your desired doneness.
Remove from the oven and let cool for 2 minutes before carefully removing the hash brown baskets from the muffin tin using a spoon or small spatula.
Serve warm.