In a large skillet over medium-high heat, add the vegetable oil until the pan is filled halfway. Once the oil is hot, add the potato slices and onion, making sure they are well-covered by the oil; add more oil if necessary. Cook for 20 minutes until the potatoes and onions are soft. Drain the oil and combine the potato mixture with the eggs. Add the salt and mix well.

In a 10-inch by 2 1/2 inch deep nonstick skillet, add the olive oil and heat over medium-high heat. Pour in the potato, egg, and onion mixture. Lower the heat to medium-low and cook for 4 to 5 minutes, until the bottom of the omelet is very light brown. Using a flat ceramic plate, cover the frying pan and flip the omelet over onto the plate. Immediately slip the uncooked side back into the pan. Cook for another 4 to 5 minutes, until the other side is a very light brown.

Remove the omelet from the pan to a plate and cut into 4 wedges.