Begin by peeling and dicing the 4 medium potatoes into small cubes. Place them in a large pot and cover with salted water. Bring the water to a boil over high heat, then reduce to medium and cook the potatoes for about 10-15 minutes, or until fork-tender. Once cooked, drain them thoroughly and set aside.

In a large non-stick skillet, melt 2 tablespoons of butter over medium heat. Once melted and bubbly, add the drained potatoes to the skillet. Allow them to cook for 5-7 minutes, stirring occasionally, until they are crispy and golden brown around the edges.

If you're using meat, stir in ½ cup of chopped cooked ham or bacon into the skillet with the crispy potatoes. Cook for an additional 2-3 minutes, stirring frequently, until the meat is heated through and the edges of the bacon are crispy.

While the potatoes and meat are cooking, crack 4 large eggs into a mixing bowl. Add ½ cup of milk along with salt and pepper to taste. Whisk the mixture vigorously until it's smooth and well combined.

Pour the egg mixture over the sautéed potatoes and meat in the skillet. Using a spatula, gently stir the mixture occasionally over medium heat for about 5 minutes until the eggs are fully scrambled.

Once the eggs are cooked, evenly sprinkle 1 cup of shredded cheddar cheese on top of the mixture in the skillet. Cover the skillet with a lid and cook for another 2-3 minutes on low heat, or until the cheese has melted.

Remove the skillet from heat and carefully uncover it. Garnish the Cheesy Potato Egg Scramble with ¼ cup of chopped green onions or chives. Serve warm.