Boil the potato in salted water about 25 minutes until tender. Drain and cool.
Peel the potato and rice it into a bowl (or mash it very well). Cool completely.
Beat the egg with the salt and optional onion and add it to the potato with the melted butter. Mix.
Add the flour. Mix well.
Lay a sheet of wax paper on your work surface. Working with a heaping tablespoon of the dough at a time, roll it between your hands until it is 3-4 inches long and a half inch thick. Bend it into a hairpin shape and place it on the wax paper. Continue in this manner with the remaining dough.
In a medium skillet heat the oil (should be about 1/2 inch) until it is hot but not smoking. Put a test chifeletto in the pan. It should fry up to a golden brown in about two minutes, turning once. Fry the remaining chifeletti in batches, remove with a slotted spoon or spatula, and drain on paper towels as they are done.