Heat some oil, enough to cover the potatoes, in a large saute pan over medium-low heat. Add the potatoes and cook, covered, until the potatoes are soft but not crispy, about 10 minutes.
While the potatoes are cooking, heat 1/4 cup olive oil in a second saute pan over medium heat. Add the onions and cook until soft and translucent, without any color, 5 to 7 minutes.
Once the potatoes and onions are soft, strain into a large bowl and drain off as much oil as possible. Set the oil aside for use in another dish.
In another large bowl, crack the eggs and whisk well. Stir in the potato and onion mixture and season with salt.
Heat 2 tablespoons olive oil in a nonstick fry pan over medium heat. When the oil is hot, add the potato and egg mixture, reduce the heat to medium-low, and cook until the eggs are set and the bottom is golden (use a spatula to peak underneath), 7 to 10 minutes.
Place a plate over the top of the fry pan large enough to cover the surface and carefully flip over the tortilla. Return the pan to the heat, add a little more oil if necessary, slide the tortilla back into the pan with the golden side facing up, and cook until the opposite side becomes golden, about 5 minutes. Flip back onto the plate, slice, and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.