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1
With a mandoline or sharp knife, slice the potatoes into 1/4-inch-thick coins. Heat the olive oil in a 9-inch cast iron frying pan over medium heat. Add the potato and onion and stir gently, then push down beneath the oil (the pan will be a bit crowded at first, but as the onions cook, the volume will decrease). Reduce the heat so the oil is bubbling gently and cook until potatoes and onions are tender but not browned, about 10 minutes. Drain into a colander set over a bowl and reserve the oil.
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2
In a large bowl, beat the eggs until well mixed. Season generously with salt and pepper and gently stir in the potato-onion mixture. In the same frying pan you used to cook the onions, heat 1 tablespoon of the reserved oil over medium heat. Arrange an oven rack about 3 inches from the broiler and pre-heat the broiler.
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3
Pour the egg-potato mixture into the frying pan, reduce the heat to medium-low, and cook until the edges of the tortilla are set and the underside is golden brown (peek to ensure the bottom isn't browning too quickly), about 5 minutes, periodically running a rubber spatula around the inner edge of the pan to prevent the eggs from sticking; the top will still be runny.
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4
Transfer the pan to the oven and broil until the top is puffed, golden brown, and set, about 3 minutes. Remove from the oven and run the spatula around the inner edge of the pan to loosen the tortilla. Invert a large plate over the pan and, in one motion, flip the pan over so the tortilla is in the plate. Let cool slightly, then sprinkle with flaky salt and serve with aioli or Fancy Mayonnaise.
