In a medium skillet heat oil over medium heat. Add potatoes in a single layer. Cover and cook for 5 to 7 minutes or until potatoes are tender, stirring once. Stir in ham.
In a small bowl beat together eggs and water with a rotary beater; pour over potato mixture. Cook over medium heat, without stirring, until egg mixture begins to set on the bottom and around edge. Using a spatula or a large spoon, lift and fold the partially cooked egg mixture so that the uncooked portion flows underneath.
Continue cooking over medium heat until egg mixture is cooked through but is still glossy and moist. Sprinkle with cheese. Remove from heat. Cover and let stand for 1 to 2 minutes or until cheese is melted. Makes 2 servings.