Peel the potatoes and cut them into even slices about 1/8 inch thick; thinly slice the onion. Keep the slices similar in thickness so they soften at the same rate.

Heat 2 tablespoons of the olive oil in a 10-inch nonstick skillet over medium-low heat. Add the potatoes and onion with about 3/4 teaspoon salt. Cook gently for 18 to 22 minutes, turning often, until the potatoes are tender when pierced and not browned hard. Lower the heat if the edges start to color quickly.

Transfer the potato-onion mixture to a colander set over a bowl and let it drain for 5 minutes. Reserve 1 tablespoon of the oil. In a large bowl, beat the eggs with the remaining salt and pepper. Fold in the warm potatoes and onion, then rest the mixture for 5 minutes so the egg coats the slices.

Wipe out the skillet if needed and heat the reserved oil over medium-low. Pour in the egg mixture and gently level it. Cook 6 to 8 minutes, loosening the edges with a spatula, until the sides are set and the underside is golden. The top will still look slightly moist.

Place a large flat plate over the skillet. Wearing oven mitts, hold the plate firmly and carefully invert the tortilla onto it. Slide the tortilla back into the skillet, browned side up. Cook 4 to 6 minutes more, until fully set. For food safety, check the center with a thermometer; egg dishes should reach 160°F (71°C). If the center is below that, continue cooking over low heat and check again.

Rest the tortilla in the pan for 10 minutes, then slide it onto a board. Serve warm or at room temperature, cut into wedges. Refrigerate leftovers within 2 hours and use within 3 to 4 days.