Heat 1 inch of water to boiling in a 2-quart sauce pan. Add potatoes. Cover bring back to boil; reduce heat to medium low. Keep covered and cook for additional 6 to 8 minutes or until potatoes are tender; drain.
Beat eggs, milk, salt, and pepper until well mixed; set aside.
Heat oil in 10-inch skillet over medium high heat. Cook potatoes in oil 3 to 5 minutes, turning potatoes occasionally, until lightly browned. Stir in green onions. Cook 1 minute, stirring constantly.
Pour egg mixture over potatoes. As egg mixture begins to set at bottom and side of skillet, gently lift cooked potions with a spatula so that the uncooked portion can flow to bottom; avoid constant stirring. Cook 3 to 4 minutes or until eggs are cooked to your liking.