Heat 1 tsp oil in each of 4 small frying pans. Add the potatoes and cook for two minutes on each side. Stir in the ham.
Crack an egg into each pan. Top with the sliced or grated cheese, sprinkle with salt and pepper and cook for 2-3 minutes until the egg is just set and the cheese is beginning to melt.
Serve sprinkled with the chopped parsley, if using.