1 cup olive oil, or a mixture of olive and salad oils
4 large potatoes, peeled and cut in 1/8-inch slices
1 large onion, thinly sliced
4 large eggs
Heat the oil in an 8- or 9-inch skillet and add the potato slices one at a time to prevent sticking. Alternate potato layers with the onion slices and salt the layers lightly. Cook slowly, over a medium flame, lifting and turning the potatoes occasionally, until they are tender but not brown. (The potatoes will remain separated, not in a "cake.")
Meanwhile, in a large bowl beat the eggs with a fork until they are slightly foamy. Salt to taste. Remove the potatoes from the skillet and drain them in a colander, reserving about 3 tablespoons of the oil. (The potatoes give the oil a delicious flavor, so reserve the rest for future use.) Add the potatoes to the beaten eggs, pressing the potatoes down so that they are completely covered by the egg. Let the mixture sit 15 minutes.
Heat 2 tablespoons of the reserved oil in a large skillet until very hot (you may use the same skillet as long as absolutely nothing is stuck on the bottom). Add the potato- and-egg mixture, rapidly spreading it out in the skillet with the aid of a pancake turner. Lower the heat to medium-high and shake the pan often to prevent sticking. When the potatoes begin to brown underneath, invert a plate of the same size over the skillet. Flip the omelet onto the plate. Add about 1 tablespoon more of oil to the pan, then slide the omelet back into the skillet to brown on the other side. (If your skillet was not hot enough, some of the omelet may stick to the pan. If this happens, don't despair--scrape off the pieces and fit them into their places on the omelet. With subsequent flips, the pieces will mesh with the omelet.)
Lower the heat to medium. Flip the omelet 2 or 3 more times (this helps to give it good shape) cooking briefly on each side. It should be slightly juicy within. Transfer to a platter and serve hot or at room temperature. I prefer it after it has been sitting for several hours. Serve with a Valdepenas or Valencia wine.