Preheat the oven to 400.
In a large well seasoned cast iron skillet melt the butter over medium heat.
Add the potatoes and cook, stirring occasionally, until tender and brown, about 15 minutes.
Add the parsley, garlic, salt and pepper to taste and remove from the heat.
Push the potatoes aside to make 4 evenly spaced shallow nests and break 2 eggs into each.
Bake until the egg whites are cooked and the yokes are still runny, about 10 minutes.
Sprinkle the cheese over the eggs and continue baking just until it melts, about 1 minute.