Heat the oil in a 9-inch skillet and add the potato slices one at a time so they don't stick together. Alternate layers of potato with the onion slices and salt the layers lightly. Cook slowly over medium heat (the potatoes will really boil in the oil rather than fry), lifting and turning the potatoes occasionally, until they are tender but not brown. The potatoes should remain separated, not in a "cake." Drain the potatoes in a colander, reserving about 3 tablespoons of the oil. ( The onion and potato give the oil a wonderful flavor, so save the rest for some other use. ) Wipe out the skillet, scraping off any stuck particles. (If this is difficult to do, wash the skillet. It will be used again to set the omelet and must be completely clean to avoid sticking.)
Meanwhile, in a large bowl beat the eggs with a fork until they are slightly foamy. Salt to taste. Add the potatoes and julienned red peppers to the beaten egg, pressing the potatoes down with a pancake turner so that they are completely covered by the egg. Let the mixture sit for 15 minutes.
Heat 2 tablespoons of the reserved oil in the skillet until it reaches the smoking point. (It must be very hot or the eggs will stick.) Add the potatoes, pepper and egg mixture, spreading it out rapidly in the skillet with the aid of a pancake turner or off-set spatula. Lower the heat to medium-high and shake the pan often to prevent sticking. When the eggs begin to brown underneath, invert a plate of the same size over the skillet and flip the omelet onto the plate. Add about 1 tablespoon more oil to the pan, then slide the omelet back into the skillet to brown on the other side.
Lower the heat to medium and flip the omelet two or three more times (this helps to give the omelet a good shape while it continues to cook), cooking briefly on each side. It should be juicy inside. Transfer to a platter and cool , then cut in thin wedges