Heat the oil in a large cast-iron or nonstick skillet over medium-high until very hot but not smoking. Add the potatoes and onion, season with salt and pepper, reduce the heat to medium, and cook, stirring occasionally and adjusting the heat if necessary so that the vegetables do not brown, until the potatoes are tender when pierced with the tip of a paring knife, 15 to 20 minutes.

Meanwhile, beat the eggs with salt and pepper to taste in a large bowl. Add the potatoes to the eggs, then pour into the skillet, spreading the potatoes evenly in the pan. Cook for about 1 minute, just to set the bottom of the egg mixture. Reduce the heat to medium-low and cook for 20 minutes, or until almost set throughout. Carefully flip the tortilla over (invert it onto a plate if you must, then slide it back into the pan, bottom side up) and cook for 5 minutes longer, until set. Flip out onto a clean plate and allow to rest for 5 minutes. Serve warm or at room temperature.