Prepare Potatoes: Boil diced potatoes in salted water for 10-15 minutes until fork-tender, then drain.

Sauté Potatoes: Melt butter in a skillet over medium heat, add boiled potatoes, and cook until golden brown and crispy, about 5-7 minutes.

Add Meat: Stir in chopped ham or bacon and heat for 2-3 minutes until warmed through.

Beat Eggs: In a mixing bowl, whisk together eggs, milk, salt and pepper until smooth.

Cook Eggs: Pour the egg mixture over the potatoes in the skillet, cook undisturbed for 1-2 minutes, then stir and cook until eggs are fully cooked, about 5 minutes.

Melt Cheese: Sprinkle cheese over egg mixture, cover with a lid, and cook on low heat for 2-3 minutes until melted.

Serve: Top with green onions or chives and serve warm.