Peel, boil, and mash the potato. Let it cool to room temperature.
Put the mashed potato in a large bowl. Add powdered sugar 1 cup at a time until the potato and sugar mixture gets to playdough consistency. You may need slightly less or slightly more than 8 cups of powdered sugar.
Dust a surface with powdered sugar. Roll the dough out to rectangle of 1/4" thickness.
Spread peanut butter over the rectangle.
Roll the dough like a log, pinching the ends to keep the filling in.
Wrap the log in plastic wrap and place in the refrigerator for 30 minutes to an hour.
Remove and unwrap the log. Use a sharp knife to cut the candy into 1/2" thick pieces.
Store in the refrigerator in an airtight container.