Heat the olive oil in a small frying pan and gently fry the onion over a medium heat until soft but not coloured. Transfer the onions to a bowl, and discard the remaining oil left in the pan.
Heat the vegetable oil in a deep heavy-based frying pan until a breadcrumb sizzles and turns golden brown when dropped into it. Alternatively, use an electric deep-fat fryer heated to 170C/325F. (CAUTION: Hot oil can be dangerous. Do not leave unattended.). When the oil is hot, add the sliced potatoes and cook until soft (test a slice by removing from the oil, and piercing with a fork – if the fork pierces the potato easily they are cooked), don’t let them go crisp and brown. Remove the potatoes from the hot oil and leave to drain on kitchen paper. Once cooled, put the cooked potatoes in the bowl with the onions and set aside.
Add the eggs to the potatoes and onions, season with salt, and gently mix with a fork to break up the potato slices slightly. Pour the potato mixture into the pan previously used for cooking onions. Flatten the mixture and cook over a low heat for about 5-10minutes, until the egg has set on the top and the bottom is starting to colour. Once the tortilla is set on the top, slide it out of the pan and onto a plate, cooked side down. Then take the pan, place it over the uncooked side of the tortilla, then swiftly turn the plate and pan over (holding onto both tightly), the tortilla will now be cooked side-up in the pan. Place the pan back on the heat and cook for a further 5 minutes until the underside is light brown. Remove from the heat.
The tortilla can be served hot or cold. Cut into slices and serve as part as a tapas selection with other Spanish-themed dishes.