Cut the potatoes into thin slices and the onions into rings.
Heat the olive oil in a heavy pan and just cook the potatoes over low heat for 10 minutes. If possible, you shouldn`t tan. Pour onto a sieve, collect the oil. Now pre-cook the onions in oil, drain them.
In a large bowl, whisk the eggs with salt and pepper. Mix in the potatoes and onions.
Heat the collected oil in the pan, add the potato mixture. Bake gently for 5-8 minutes until the mixture is almost thick.
Hold a plate upside down over the pan and turn the tortilla out onto it. Let the turned tortilla slide back into the pan. Bake on low heat for 2-3 minutes or more until the underside is golden brown.
Cut into pieces of cake and serve garnished with flat-leaf parsley.