Combine mashed potatoes, butter, and one cup of sugar in a large bowl and use an electric mixer to stir until combined.
Add remaining sugar, 1 cup at a time and stirring until combined after each addition. Once you've added 6 cups of powdered sugar, check the consistency. If the dough is not moldable in your hands and can't be rolled into a ball, continue to add sugar until it is firm.
Stir in vanilla extract.
Refrigerate for at least 1 hour (if you chill longer it may become too firm and brittle and will just need to sit at room temperature for 10-15 minutes until it is pliable).
Once chilled, divide dough into two pieces and place one piece on a clean surface that you've generously dusted with powdered sugar. Dust the surface of the dough with additional sugar, and use a rolling pin to roll dough out into a rectangle about ¼" thick. If your dough is too sticky or falling apart, you may need to add more sugar, re-shape it into a ball, and start over.
Once dough has been rolled into a ¼" thick rectangle, spread evenly with peanut butter, leaving a small amount of space peanut butter-free around the perimeter of the dough.
Starting with the longer side of your rectangle, gently but tightly roll into a log.
Use a knife to slice into pieces about ¼-½" thick.
Repeat steps 5-8 with remaining half of dough.
Serve and enjoy. Store leftover candy in an airtight container in the refrigerator for up to a week.
* Use russet potatoes, peel, dice, and boil until tender. Drain potatoes and then mash well. Allow potatoes to sit at room temperature until completely cooled before making your filling. You want to use just the potatoes, unseasoned, no milk/salt/pepper/etc. added. Thanksgiving leftovers unfortunately would not work well for this recipe.
Another (peanut butter-free) version of this candy can be made by rolling the filling into cigar shapes and rolling in 2 Tablespoons of cinnamon for Cinnamon Cigar Candy.I've also used this potato candy recipe to make my old fashioned Easter Egg Candy.