Heat 2 tablespoons of olive oil in an 8- or 9-inch skillet over medium heat.

Add the potatoes and onions in alternating layers, seasoning each layer with salt.

Cook, turning occasionally, until the potatoes are tender but not browned, for about 20 minutes.

Drain in a colander and set aside.

Reserve 2 teaspoons of the oil and wipe the skillet clean.

In a large bowl, lightly beat the eggs with a pinch of salt.

Add the cooked potatoes and onions, ensuring they are well coated.

Allow the mixture to sit for about 15 minutes to absorb the flavors.

Heat 2 teaspoons of reserved oil in the skillet over medium-high heat until it's hot but not smoking.

Pour the egg and potato mixture into the skillet, spreading it evenly.

Reduce the heat to medium-high and cook, occasionally shaking the skillet to prevent sticking, until the bottom begins to brown.

Place a plate larger than the skillet over the top.

Flip the skillet to transfer the omelet to the plate.

Heat the remaining 1 tablespoon of oil in the skillet over medium heat.

Slide the omelet back into the skillet to cook the other side, shaking occasionally, until set in the center but still slightly moist inside.

Once cooked to your liking, slide the omelet onto a serving plate.

Cut it into wedges and serve either warm or at room temperature.