Place the diced potatoes in a microwave-safe bowl with 1 tablespoon of water. Cover and microwave on high for 4-5 minutes until just tender but not fully cooked. Drain any excess water and pat dry with a paper towel.

Heat 1 tablespoon of oil in a large non-stick skillet over medium-high heat. Add the par-cooked potatoes and cook for 6-8 minutes, stirring occasionally, until golden brown and crispy on the edges. Add the diced ham and the white parts of the green onions. Cook for another 2-3 minutes until the ham is lightly browned. Transfer the potato-ham mixture to a plate.

Reduce heat to medium-low. Add the remaining 1 tablespoon of oil and the butter to the same skillet. Pour in the beaten eggs. Let them set for 30 seconds, then gently push the cooked edges toward the center with a spatula, allowing the uncooked eggs to flow to the edges. Continue until eggs are softly set but still slightly wet.

Return the potato-ham mixture to the skillet with the eggs. Sprinkle with garlic powder, paprika, pepper, and salt. Gently fold everything together. Sprinkle 3/4 cup of the shredded cheddar cheese over the top. Cover the skillet with a lid and let it cook for 1-2 minutes, or until the cheese is fully melted.

Remove the skillet from heat. Sprinkle the remaining 1/4 cup of cheese and the green parts of the sliced green onions over the top. Spoon the hot scramble into individual black bowls and serve immediately.