Prepare all ingredients. Set out a deep non-stick frying pan, a large bowl, a slotted spoon and a flat plate or pan lid for turning the tortilla. Peel the potatoes and wash them thoroughly under cold water. Dry the washed potatoes carefully so that as little water as possible reaches the hot oil. Cut the potatoes into thin, evenly sized slices. Peel the onion, cut it in half and slice it finely.

Pour the olive oil into the deep frying pan and heat it over medium heat. The oil should be hot but not smoking, because the potatoes should cook slowly rather than immediately becoming crisp. Carefully add the potato slices to the warm oil. Add the finely sliced onion to the potatoes. Gently combine the potatoes and onions so everything is evenly coated with oil. Cook the mixture slowly over medium-low heat. Turn the potatoes and onions regularly with a slotted spoon so they soften evenly and do not stick to the bottom of the pan. Use the slotted spoon to break up any overly large potato pieces while they cook. Cook the potato and onion mixture until the potatoes are tender and beginning to turn lightly golden.

Prepare a heatproof bowl and lift the cooked potatoes and onions from the oil with the slotted spoon. Allow the potato and onion mixture to drain thoroughly. Carefully pour the excess olive oil from the pan into a heatproof container and reserve it for a later step.

Crack the eggs into a large bowl. Add a generous pinch of salt to the eggs. Beat the eggs thoroughly with a fork or whisk. Add the drained potatoes and onions to the beaten eggs. Gently combine everything without completely crushing the potatoes. Allow the mixture to rest for a few minutes so the eggs, potatoes and onions combine well.

Return the frying pan to the stove and coat the base with a small amount of the reserved olive oil. Heat the oil over medium heat. Pour the entire egg and potato mixture into the pan. Spread the mixture evenly with a spatula and gently round the edges. Reduce the heat to low and cover the pan with a lid. Allow the tortilla to set slowly for about five to ten minutes, until the underside is golden and the top is mostly set. Carefully loosen the edge with a spatula and check whether the underside is sufficiently browned.

Place a large flat plate or suitable lid completely over the frying pan. Hold the plate and pan firmly and turn the tortilla over with one quick, careful movement. Add another small amount of olive oil to the pan if needed. Carefully slide the turned tortilla from the plate back into the pan. Cook the second side slowly over low heat until set and golden. Shape the edge lightly with a spatula and check whether the tortilla has reached the desired level of doneness.

Slide the finished tortilla onto a round plate or serving platter. Allow the tortilla to rest for a few minutes so it is easier to slice. Serve the Spanish omelette hot, warm or cold, cut into wedges or small tapas-style cubes.