Peel and cut the potatoes into thin slices (about ¼ inch thick).
In a 10-inch nonstick pan, heat the oil over medium heat.
Stir in the potatoes, onion, and ¾ teaspoon of salt. Let cook, stirring occasionally, for about 15 minutes, or until the potatoes are tender. Transfer the potatoes to a bowl and let cool for about 5 minutes.
In a separate large bowl, whisk the eggs with the remaining salt and pepper. Stir in the potatoes and combine.
Drain the oil from the pan leaving just about 2 tablespoons oil in the pan. Return the pan to the heat.
Pour the potato and egg mixture into the pan. Shake the pan slightly to level the ingredients. Let it cook, without stirring, for about 5 minutes, or until the eggs begin to set close to the center. While this is taking place, run a silicone spatula around the edges pressing in a bit to create the round shape of the tortilla.
Invert a large flat plate over the pan and in one quick motion flip the tortilla onto the plate. (It’s best to do this over the sink in case there are any spills. Also, use a towel under the plate. Remember the tortilla and the pan are hot!) Then, slide the tortilla back into the pan to cook on the other side.
Let the other side cook for about 3 - 5 minutes, or until the tortilla smoothly slides around when you shake the pan.
Slide the tortilla onto a clean plate and cut it into eight slices.
Serve warm.