Wash and peel the potatoes. Dry with a cloth or paper towel and cut into thin slices of 1/8 inch.
Heat the oil in a skillet over low heat. Add the potatoes and cover to cook, moving them every 4 or 5 minutes. Repeat this until they are soft, and add a little salt.
Once cooked, strain them in a colander to remove excess oil and reserve.
In a bowl, beat the eggs with a fork; they don’t have to be completely combined, just well mixed. Add a little salt and pepper (remember that the potato is already salted). Add the potatoes and mix well.
In a medium nonstick skillet (about 10”), heat two tablespoons of olive oil (or enough to cover the bottom) over medium heat. When hot, add the mixture of eggs and potatoes. Move the pan so that the omelette does not stick. If necessary, lower the heat to medium-low.
Cook until the mixture takes on a golden color, approximately 4 minutes. Place a dish on the pan and turn it over to remove the omelette.
Add a spoonful of olive oil to the pan and place the omelet in the pan again to cook the other side. Cook for about 2 minutes, making sure to move it so that it does not stick.
Once cooked, remove it to a dish again and let it rest for 10 minutes before serving.