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. They may break down a little; this is okay.
While the potatoes are cooking, beat the eggs in a large bowl and season with some salt.
Slice the onion as very thinly, and fry it in oil over medium heat in a separate pan until it begins to caramelize, about 10-20 minutes. Add a splash of water now and then to deglaze and prevent burning. Drain off any excess oil and add to the egg mixture.
Once the potatoes have fried for 20 minutes, remove them with a skimmer or spider 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. Some uncooked egg mixture will likely slip out, but that's okay. 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.