In 10-inch omelet pan or skillet over medium heat, cook potatoes, pepper, onion, olives and 1/3 cup of water, covered, until potatoes are soft, about 7 to 8 minutes.
Drain, if necessary. Remove all but 2 tablespoons of vegetable mixture from pan and set aside. Add oil. Raise heat to medium-high.
In small bowl, beat together eggs and remaining 2 tablespoons water until well blended. Pour over vegetables in pan. (Mixture should set immediately at edges.) With an inverted pancake turner, carefully push cooked portions at edges toward center so uncooked portions can reach hot pan surface, tilting pan and moving cooked portions as necessary. When top is thickened and no visible liquid egg remains, fill one half of omelet with reserved cooked vegetables, cheese and chopped parsley. With pancake turner, fold omelet in half. Invert onto plate with quick flip of wrist, or slide from pan onto plate. Garnish with parsley sprig, if desired.
*For even faster cooking, substitute 2/3 cup (about 2.5 oz.) frozen diced potatoes for fresh potatoes. Reduce water to 5 tablespoons, divided. In 10-inch skillet over medium heat, cook frozen diced potatoes with pepper, onion, olives and 3 tablespoons of the water, covered, until potatoes are soft, about 3 to 4 minutes. Proceed with recipe.