Heat the oil in a non-stick pan and cook the potatoes for 8-10 minutes until nearly cooked and beginning to brown. Add the onion and continue to cook until the onion is just golden, then add the garlic. When the potatoes are just cooked, season the egg mixture and add to the potatoes. Stir well and allow the eggs to cook on the base. Place a plate over the pan, carefully turn the omelette onto the plate, then slide back into the pan to cook the other side.
To serve, sprinkle with parsley and cut into wedges. Note You can add other ingredients, whatever is available - chopped ham, bacon, scallions, mushrooms. You can of course use up cooked potatoes, but the flavour is much better if you start out with uncooked.