Heat 2 cups of extra-virgin olive oil in a deep stockpot over medium-high heat until almost smoking, 2 to 4 minutes. Add potatoes and onion, ensuring they are mostly covered with oil. Season with 1 ½ teaspoons of salt. Cook while stirring occasionally and maintaining a gentle simmer until the potatoes are just fork-tender, about 8 to 12 minutes.

Drain the potato-onion mixture in a colander, reserving the oil for another use or discarding it. Let cool for a few minutes, then taste and adjust seasoning with more salt if needed.

In a large bowl, crack the eggs and season with the remaining 1/2 teaspoon of salt. Whisk until well beaten, then add the potato-onion mixture. Toss to coat evenly.

Heat 1 teaspoon of olive oil in a 10-inch nonstick skillet over high heat. Pour in the egg-potato mixture, level it with a spatula, and cook for 1 minute. Reduce the heat to medium-low and continue cooking for about 5 minutes, running a spatula around the outer edges to prevent sticking and give the tortilla shape.