Dry the potato slices on paper towels. Heat the oil in a non-stick skillet. I used 9-inch (23cm) skillet, because I didn't have a smaller one, but you can use 8-inch (20cm) or even 7-inch (18cm) skillet if available. Add the potato slices and onion, and cook covered, over low heat, stirring occasionally, for 20-30 minutes. Potatoes should be tender when you prick them with a fork. Remove the potatoes and onion from skillet, draining them in a colander. Put on paper towels. Discard the oil.
In a bowl, beat the eggs. Add the potatoes and onion, and combine. Season with salt and pepper.
Heat 1 tablespoon olive oil in the same skillet. Add the egg, potato and onion mixture and cook for 3-4 minutes, on a low heat. Shake the pan occasionally to avoid sticking. Place a slightly bigger lid or a plate on top of the skillet and invert it quickly, flipping the omelette on to the lid.
Heat another tablespoon olive oil in the same skillet and slide the omelette back in. Cook for 2-3 minutes more over low heat. Enjoy!