Peel potatoes. Cut in half lengthwise and slice into approx. 1/4" slices. Set aside.
Peel onion. Cut in half lengthwise and slice the same thickness or slightly thinner than potatoes. Add to potatoes.
Heat all the olive oil over medium heat in a frying pan large enough to hold the oil, potatoes and onion. Heat for 2-3 minutes. To check if it's ready put a slice of potato in the oil. It should be sizzling gently. Add all the potatoes and onion. Stir, making sure everything is coated in oil.
Cover with a lid and continue cooking for approximately 20 minutes. Check and stir carefully every few minutes making sure the oil isn't getting too hot. It should be simmering gently. The potatoes and onions are done when you can easily break apart the potato with a wooden spoon or spatula.
Drain in a colander over a bowl to catch the oil. Set aside the collected oil. Whisk together the eggs and salt. Add the potatoes and onions to the egg mixture stirring well but gently. Let sit for 10 minutes.
Heat 1 tbsp of the reserved olive oil in the finishing size frying pan over medium-high heat. Add the potato, egg mixture moving it around slightly to distribute the egg evenly. Turn the heat down to medium. Without stirring, cook for 6-7 minutes, checking the bottom by lifting the edge up slightly with a spatula.
When nicely browned on the bottom remove from heat. Place a larger sized plate or tray on top. Over the sink. with one hand holding the pan handle and the other on top of the plate, carefully flip the pan over so the omelette is cooked side up on the plate. Wipe the pan with paper towel and heat up another 1 tbsp of olive oil on medium-high heat. Gently slide the omelette back into the pan with the cooked side up. Reduce the heat to medium. Using a wooden spoon or spatula push the sides in slightly to create a rounded edge. Continue cooking for 3-4 minutes or until the bottom is nicely browned and the center is firm and set. You can always return it to the pan to brown either side a little more if necessary. Let cool for at least 20 minutes before eating but ideally an hour or more to give it time to set.