Preheat oven to 400°. In a 10-in. cast-iron or other ovenproof skillet, heat butter over medium-high heat. Add potatoes; cook and stir until golden brown and tender. Stir in parsley, garlic, salt and pepper. With the back of a spoon, make 4 wells in the potato mixture; break 2 eggs into each well., Bake until egg whites are completely set and yolks begin to thicken but are not hard, 9-11 minutes. Sprinkle with cheese; bake until cheese is melted, about 1 minute.