Heat 3 tablespoons of olive oil in a large non-stick frying pan (about 20-22cm) over medium heat. Add the sliced potatoes and onion.
Cook gently for 15-20 minutes, turning occasionally, until the potatoes are tender and the onion is soft and sweet. Do not let them brown too much - low and slow is the way.
Drain off any excess oil from the pan. Season the potato and onion mixture well with salt.
Beat the eggs in a large bowl, season with salt and pepper. Add the potato and onion mixture and stir to combine. Let it sit for 5 minutes so the potatoes absorb some egg.
Wipe the pan clean, add the remaining tablespoon of oil and heat over medium heat. Pour in the egg and potato mixture and smooth the top.
Cook for 5-6 minutes on medium-low heat until the edges are set and the bottom is golden. Place a plate over the pan, flip the tortilla onto it, then slide it back in to cook the other side for 3-4 minutes.
Let it rest for 5 minutes before slicing. Serve warm or at room temperature with a side salad.