Peel the potatoes and rinse them under cold water. Slice them thinly (about 5 mm thick) using a sharp knife or mandoline.
Pat the potato slices dry with paper towels and put them into a large bowl, then sprinkle with salt and mix well.
Heat a ½ inch of high quality extra virgin olive oil in a large frying pan over medium low heat. When the oil is hot, add the potatoes and add more oil if necessary until all are covered.
Cook the potatoes on low heat for 20 minutes.
Crack the eggs into a large bowl and season with some salt. Beat them well.
Slice the onion thinly. In a separate pan, heat 1/4 cup olive oil over medium heat. Add onions and cook for about 20 minutes until they begin to turn caramel-colored. Add a little water if they start to stick. Drain off any excess oil and add to the egg mixture.
Once the potatoes are soft but not mushy (about 20 minutes), remove them with a slotted spoon into a colander and allow them to cool and drain for at least 5 minutes.
Once the potatoes have cooled, add the potatoes and onions to the egg mixture and stir well. Let the egg mixture sit for about 15-20 minutes.
*Pour out the frying oil from the potatoes and save it for another use. Place the pan over medium-low heat and pour in the egg mixture.
Cook over medium-low heat for about 6-8 minutes. Make sure the heat is low enough or the tortilla will cook too quickly and be rubbery. You can run a rubber spatula along the edges to make sure the tortilla isn't sticking.
To flip the tortilla, take a large plate and put it over the pan and flip quickly. Do this with certainty and confidence. If a little spills don't sweat it. Slide the tortilla back into the pan to cook the other side, and cook for another 6-8 minutes.
Slide the tortilla out of the pan onto a serving plate and let cool a little before slicing and serving.