Rinse the potatoes in cold water and then lay them out on a clean tea cloth. Dry thoroughly. Select a large skillet and add a good layer of oil. I tend to use a combination of sunflower oil and olive oil, but the traditional recipe will use only olive oil. Get the oil hot in the skillet and then add the potatoes in a single layer. Turn the heat down a bit and keep an eye on them, turning them every once in a while to get nice crunchy, evenly golden chunks of potatoes. Try to avoid moving them around a lot as this will break the potatoes up. You want nice chunks in the final tortilla. When the potatoes are completely cooked through, use a slotted spoon and place the potatoes on a baking tray that has been lined with paper towels. This will absorb some of the excess oil. Sprinkle with a little sea salt.
Break the eggs into a bowl and lightly whisk with a fork. Add the potatoes,a little more salt and pepper. Discard the oil left in the skillet and then use a paper towel to wipe out the pan, removing any little crusty bits. These are likely to burn if left in the pan. Add a few glugs of olive oil into the skillet and heat through. Add the potato and egg mixture. Turn the heat down to low and allow the tortilla to cook through. Every once in awhile give it a little jiggle. When the tortilla looks set, which can take about 20 minutes, place a clean plate over the skillet and flip the tortilla out. Place it back in the skillet, adding a little more oil if necessary and cook for a few more minutes. Remove from the heat and flip back onto a clean plate. You can serve this hot, warm or at room temperature, cut into chunks or wedges.