Place diced potatoes in salted water and bring to a boil over medium-high heat. Cook 10–15 minutes until fork-tender, then drain and set aside.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add the boiled potatoes and cook 5–7 minutes, stirring occasionally, until the edges turn golden and slightly crispy.

If using, stir in chopped cooked ham or bacon and cook 2–3 minutes until heated through and lightly caramelized.

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

Pour the egg mixture over the potatoes in the skillet. Let cook 1–2 minutes undisturbed, then stir gently occasionally until eggs are scrambled and set but still soft.

Sprinkle shredded cheddar evenly on top. Cover the skillet and cook 2–3 minutes until the cheese melts fully.

Remove from heat, sprinkle with chopped green onions or chives, and serve warm. Enjoy your cheesy, hearty breakfast!