Heat oven to 350°F.
Spray a 2-quart square baking dish with cooking spray.
Arrange potatoes evenly in the bottom of the dish.
Sprinkle with cheese, ham, and green onion.
In a medium mixing bowl, combine eggs, milk, pepper, and salt.
Pour egg mixture over potato mixture in the dish.
(The dish may be covered and refrigerated at this point for several hours or overnight.)
Bake uncovered for 40 to 45 minutes (or 55 to 60 minutes if made ahead and chilled) or until the center appears set.
Let stand 5 minutes before serving.