In a small pot of boiling water, cook the potato until tender. Drain and transfer to a bowl; mash until smooth and lump-free. Let cool completely.
With an electric mixer on low speed, beat together the potato and powdered sugar, one cup at a time, until mixture is thick and the pearly dough forms.
Transfer the dough onto a large sheet of parchment paper sprinkled with powdered sugar; dust more powdered sugar on top. Using a rolling pin, roll the dough into a large rectangular shape, approximately ¼-inch thick; trim to form straight edges.
Spread peanut butter over dough (see recipe notes). Starting at one long side, tightly roll up candy, jelly-roll style, using parchment paper as a guide. Wrap in parchment paper or plastic wrap, and freeze or refrigerate for 30-60 minutes.
Unwrap and cut candy into ¼-inch thick pieces. Enjoy! (See the post for storing the leftover candy)
Work quickly as the dough dries fairly fast. If your dough begins to harden, wet your hands with a small amount of water and knead the dough back to the proper consistency.
When spreading the peanut butter, leave a ¼-inch edge. Otherwise, the peanut butter will seep out and make a messy roll.
The amount of sugar needed depends on the moisture level and the size of your potato. You should have about ⅓-1/2 cup of mashed potato but don't worry if you're over or under. Just add less or more sugar for the right consistency. Your dough should be slightly firmer than cookie dough.
If you have peanut allergies, use nut-free sun butter or almond butter if tolerated. Cookie butter is another option. (It's made from pulverized cookies, butter or condensed milk, and sugar).
You can add a teaspoon of vanilla extract to the mashed potato if you wish.
Separate the dough into 2, 3 or 4 even pieces if you'd like a mixture of candy - with different filling or color (see ideas in the post).
If you're making more than one roll, slice them into ½-inch thick pieces (as rolls will be smaller), otherwise slice one big roll into ¼-inch thick pieces.