Grease a 3-quart rectangular baking dish. Arrange potatoes evenly in the bottom of the dish. Sprinkle with cheese, ham, and green onion. In a large mixing bowl, combine eggs, milk, salt and pepper. Pour egg mixture over potato mixture in dish.
At this point, you can cover and refrigerate until ready to bake (several hours or overnight). When ready to bake, preheat oven to 350°F. Bake, uncovered, for 1 hour and 15 minutes or until the center appears set. Let stand for 5 minutes before serving. If baking after casserole has been chilled, you will need to increase baking time to 1 hour and 30 minutes.