In a deep-fryer or a deep pot, heat the oil to 350 degrees. (A deep-frying thermometer can be clipped to the side of the pan so that you can tell when the proper temperature has been reached).
Meanwhile, in a large saucepan bring 2 quarts of water to a boil. Add the pecans and boil for 2 minutes. Drain in a large strainer, shaking off all excess water. Sprinkle the salt and cayenne pepper over the nuts and then coat with the confectioners' sugar, a little at a time, allowing the sugar to melt into the pecans. Toss the nuts by shaking the strainer, adding a little more sugar each time, until all the sugar is used and all the nuts are coated. Do not use hands or a spoon to toss. The nuts should have a glaze of sugar.
Carefully add the nuts to the heated oil, keeping the oil at 350 degrees F. Cook until golden brown, about 3 minutes, stirring occasionally. Remove with a slotted spoon to a baking tray to cool.