Peel the potatoes.

Quarter the potatoes lengthwise and thinly slice them crosswise.

Heat almost all of the olive oil in a large skillet until shimmering.

Carefully add the potatoes to the skillet.

Cook over high heat, stirring occasionally, until the potatoes are softened and just beginning to brown, about 15 minutes.

Transfer the potatoes to a colander to drain.

Pour off most of the oil in the skillet, leaving a thin layer.

Return the skillet to high heat and add the remaining oil.

In a large bowl, combine the potatoes with the beaten eggs and season with salt.

Add the potato-egg mixture to the skillet.

Cook, lifting the edge of the tortilla and tilting the pan to allow the uncooked eggs to seep underneath, until the bottom is golden and set, about 5 minutes.

Slide the tortilla onto a large plate.

Pour off any excess oil.

Cover the tortilla with the inverted skillet.

Using oven mitts, grasp the skillet and the plate and quickly invert the tortilla back into the pan.

Cook the tortilla over high heat until the bottom is set and lightly browned, about 2 minutes longer.

Slide the tortilla onto a plate.

Cut into wedges and serve.