Preheat the oven to 400°F (200°C).
In a large bowl, combine the thawed shredded hash browns, salt, and black pepper. Mix well.
Brush a 6-cup muffin tin with the melted butter to prevent sticking.
Divide the hash brown mixture evenly among the muffin cups, pressing it firmly and evenly up the sides to form baskets.
Brush the tops of the hash brown baskets with the remaining melted butter.
Bake the hash brown baskets in the preheated oven for 15 minutes, or until they are golden brown and crispy.
Carefully remove the muffin tin from the oven. Crack one egg into each hash brown basket.
Sprinkle the shredded cheddar cheese evenly over the eggs.
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 the hash brown baskets from the oven and let them cool for 2 minutes.
Garnish each basket with chopped fresh chives before serving.