Heat 3 tablespoons oil in heavy medium nonstick skillet over medium-low heat. Layer potatoes and onion in skillet, seasoning each layer with salt and pepper. Cover and cook until vegetables are tender, turning once, about 15 minutes. Cool 5 minutes.

Beat eggs to blend in medium bowl. Add potato mixture and mix well. Heat same skillet over medium-low heat. Add remaining 1 tablespoon oil. Pour egg mixture into skillet. Cook until bottom is just golden and top is still unset, occasionally lifting edges of omelet with spatula and tilting pan to let uncooked egg run underneath, about 5 minutes. Loosen egg and slide onto large plate. Invert plate, returning eggs cooked side up to skillet, and cook until eggs are fully set, about 3 minutes longer.