In a 10-inch skillet heat cooking oil over medium heat. Carefully add frozen potatoes. Cook about 8 minutes or until potatoes are done, turning occasionally. Drain on paper towels.
Drain all but about 1 tablespoon of oil from skillet. In a mixing bowl beat together the eggs, milk, and oregano.
Add egg mixture to skillet. Cook, without stirring, over medium heat until mixture begins to set on bottom and around edges. Using a large spoon or spatula, lift and fold partially cooked eggs so uncooked portion flows underneath. Sprinkle cooked potatoes over eggs. Continue cooking over medium heat for 2 to 3 minutes or until eggs are cooked throughout but are still glossy and moist. Remove from heat and sprinkle with cheese. Makes 4 servings.