Pour olive oil into a 10- to 12-inch nonstick ovenproof frying pan over medium-high heat; when hot, add onion and stir often until limp, about 5 minutes. Add potatoes, 1/2 teaspoon salt, and 1/4 teaspoon pepper; mix to coat. Add 1/3 cup water and bring to a boil; reduce heat to medium, cover, and cook until potatoes are tender when pierced, about 10 minutes. If any liquid remains in pan, boil, uncovered, until evaporated, 1 to 2 minutes.
Meanwhile, in a large bowl, beat eggs with 1/4 teaspoon salt and 1/4 teaspoon pepper to blend. Add potato mixture and mix gently. Place unwashed frying pan over medium-high heat; when hot, pour in egg mixture. Reduce heat to medium-low and cook until eggs begin to set and bottom is lightly browned, 5 to 8 minutes.
Transfer pan to oven and broil tortilla about 6 inches from heat until top is set, 3 to 5 minutes. Run a spatula between tortilla and pan to loosen; invert tortilla onto a plate. Cut into wedges and serve warm or at room temperature.