In a small pot of boiling water, cook the potato until tender. Drain and transfer to a bowl, then mash until smooth and lump-free; a ricer is ideal. Measure 1/2 cup. Let it cool slightly, but keep it warm.

In an extra large bowl, combine the 1/2 cup mashed potato and 2 cups of the powdered sugar until blended. At this point it will be very loose. Stir in the vanilla.

Keep adding the powdered sugar 1 cup at a time until the mixture forms a putty-like dough. Use a handheld electric mixer if stirring with a wooden spoon gets too hard. Shape the dough into a round.

Set the dough on an 18x12-inch sheet of wax paper sprinkled with powdered sugar and sprinkle the top with a little more. Roll it with a rolling pin into a rectangle about 1/4 inch thick, then trim the edges straight.

Spread an even layer of peanut butter over the whole surface of the candy.

Slowly roll the candy up from one long edge to the other. Wrap it in the wax paper and cut it in half. Put the halves in a resealable plastic bag and chill until firm, about an hour.

Slice the rolled candy into 3/4-inch pieces and serve.