I ran this as a special at work on Saturday morning and sold a lot of them. I made one for myself and tried to sit down and eat it, but the staff got their hands on it and ate it all before me. But they said it was one of the best that I have made! I won't tell them that it was not my recipe!
Melt butter in a 10-inch non-stick fry pan. Add potatoes and onion; cover and cook over medium heat for 20 minutes, stirring now and then to brown evenly, or until potatoes are tender and golden brown. Add ham; heat through, then sprinkle with parsley (if using).
Beat eggs, milk, salt and pepper together in a bowl. Pour over the potato mixture. Cover pan and cook 10 minutes or until eggs are almost set. Uncover pan and check often with a spatula; lift around edge of eggs and allow egg mixture to run under omelette during cooking. Sprinkle with cheese. Cover and cook until cheese melts. Cut into wedges and serve.