In a large, heavy, non-stick frying pan, heat the olive oil on medium-high heat. Drop a single piece of potato into the oil to ensure it is hot enough to fry. Carefully place the potato and onion mixture into the frying pan, spreading them evenly over the surface. The oil should almost cover the potatoes.
Note: If the oil is too hot, the potatoes will brown rapidly on the outside, but still be raw on the inside. You may need to turn down the heat slightly, so the mixture does not burn.
Leave in pan until the potatoes are cooked. If you can poke a piece of potato with a spatula and it easily breaks in two, your potatoes are done. Remove from the pan with a slotted spoon or spatula. Some cooks place the potato and onion mixture in a colander for a few minutes to allow more oil to drain. If you do this, place a plate underneath to catch the olive oil and you can use it again.