Heat the oil in a large skillet over medium heat and add the potato slices alternately with the sliced onion, little by little and stirring as they are added, until all slices are coated with the oil. Cook, stirring gently occasionally, until the potato slices are uniformly tender but not brown. Remove the potato and onion slices with a slotted spoon and transfer to a colander to drain. Reserve 3 tablespoons of the cooking oil separately for the omelet. The remaining oil may be strained and used for another purpose.

In the same skillet, add the chorizo and cook over medium-high heat until the sausage is browned and the fat is rendered, about 4 minutes. Remove from the heat.

In a large bowl beat the eggs until slightly foamy. Add the salt, garlic and red pepper flakes. Stir to combine. Add the potato-onion mixture from the colander and the rendered chorizo and stir gently to combine. Let sit for 15 minutes.

Heat 2 tablespoons of the reserved oil over high heat in a clean 9 or 10-inch nonstick skillet and, when very hot (smoking), add the egg-potato mixture and, using the back of a spoon or a spatula, spread the potatoes evenly in the skillet, pressing down to condense. Reduce the temperature to medium-high and cook, shaking the pan often to prevent sticking. When the omelet begins to brown underneath, invert a plate of the same or slightly larger diameter over the skillet and, working quickly and very carefully, invert the skillet to release the omelet onto the plate. Add the remaining tablespoon of oil to the skillet, then slide the omelet back into the pan and cook until beginning to brown on the second side. Continue cooking the omelet, flipping occasionally, until golden brown on both sides and cooked through, 20 to 22 minutes in total from start to finish. Transfer the omelet to a platter and set aside to cool. Cut into thin wedges or squares and serve with the Spanish Garlic and Pimento Mayonnaise. Serve either warm or at room temperature.