Bring a large pot of salted water to a boil. Add diced potatoes and cook for about 10–15 minutes until fork-tender. Drain and set aside.

Melt butter in a large skillet over medium heat. Add boiled potatoes, cooking for 5–7 minutes until golden and crispy.

If using, stir in chopped ham or bacon to the skillet. Cook for an additional 2–3 minutes until heated through.

In a bowl, beat together eggs, milk, salt, and pepper until smooth.

Pour the egg mixture over the potatoes and meat. Cook for about 5 minutes, stirring gently until just set.

Sprinkle cheese over the mixture, cover, and cook for an additional 2–3 minutes until melted.

Remove from heat and garnish with chopped green onions or chives. Serve warm.