Peel potatoes, cut in half vertically and slice with a sharp knife or mandoline to quarter-inch thickness. Thinly slice onions.

Heat 1 cup of olive oil in an 8- or 9-inch nonstick skillet over medium heat. After three to four minutes, drop in a potato slice. If it bubbles around the edges, the oil is ready. Add all potatoes, onions, 1/4 teaspoon salt and a dusting of pepper. Carefully coat mixture in pan with oil, using a wooden spoon or heatproof spatula. Adjust heat to medium-low so the oil bubbles gently. Cook, turning the potatoes every few minutes,until they are knife tender but not browned. This should take 10 to 15 minutes. If potatoes begin to break, they have cooked too long. Drain the potatoes in a colander, reserving oil.

Beat the eggs in a large bowl, adding the remaining salt and pepper to taste. Wipe out the skillet and return to medium heat. Add 2 tablespoons of the cooking oil to the pan. Mix the warm potatoes and onions into eggs, stirring to coat, then add all to the skillet. As soon as the edges firm up, about two minutes, reduce heat to medium-low and cook for five minutes.

Run a heatproof rubber spatula all around the edge of the tortilla to ensure it will release from the pan. The top will still be runny, not set. Carefully slide the tortilla onto a dinner plate. Cover with another plate and, holding plates tightly together, flip them so the runny egg side is on the bottom. Add 1 more tablespoon of oil to skillet and carefully slide the tortilla back into the pan. Cook five more minutes, then slide onto a clean plate for serving.