Place potato in a small pot, cover with water, and boil until very tender. Drain and transfer to a large bowl. Mash (or use a hand mixer) until smooth and lump-free.
Add4 cups powdered sugar and mix until blended (will be a sticky mess and this point). If opting to use vanilla, mix in now. Mix in more powdered sugar, 1 cup at a time, until mixture is very thick (slightly thicker than cookie dough).
Laydown a large sheet of wax paper and sprinkle generously with powdered sugar. Transfer candy mixture to the wax paper and sprinkle the top with more powdered sugar. Roll out to 1/4 inch thick rectangle.
Spread peanut butter evenly over candy. Roll tightly (long side toward long side),then wrap in the wax paper. Cut in half crosswise and put the two halves inside a large re-sealable bag. Seal the bag and chill for at least 30 minutes until firm, or until about 30 minutes before ready to serve.
Unwrap candy and slice into 1-inch thick slices and serve or store in airtight container, chilled, up to 2 weeks.