Slice the potatoes very thinly and toss them in a bowl with a little seasoning. Heat the oil in a medium-sized, heavy-based frying pan. Add the potatoes and fry them very gently for 10 minutes, turning them frequently until they are softened but not browned.
Add the onions and fry them gently for a further 5 minutes without browning. Spread the potatoes and onions in an even layer in the pan and turn the heat down as low as possible.
Pour over the eggs, cover and cook very gently for about 15 minutes until the eggs have set. (If the centre of the omelette is too wet, put the pan under a moderate grill to finish cooking.) Tip the tortilla on to a plate and serve warm or cold.