Heat oil in a heavy-bottomed, non-stick frying pan over medium heat. Sauté onion until just softened, then add sliced potatoes. Boil in oil until potatoes are soft but not browned. Remove the potatoes and onions from heat and cool on plate, roughly 10 minutes. If the mixture is sitting in too much oil, pour excess oil back into the frying pan.
Crack eggs into a large bowl and beat. To the eggs, add cooled potato, onion, salt, and pepper, mixing together gently to combine. Warm the oil used to fry the potatoes and onions over medium heat. Add the egg mixture to pan and shake to keep the eggs from sticking. Cover and let cook until the top is nearly set.
When the eggs are almost fully cooked, flip the tortilla onto a plate, placing the plate on top of the pan and inverting. Slide the tortilla off the plate and back into the pan to finish cooking what was the top. Cook an additional 5 minutes. Remove from heat and cool before serving; room temperature is best.