Step 1

Use a fork to prick the potato all over. Place on a microwave-safe plate and microwave until easily pierced with a paring knife, 8 to 10 minutes, rotating halfway through. If the potato is still too firm, continue to cook in 1-minute increments. Cut the potato in half and let cool until easy enough to handle, about 5 minutes. Scoop out the flesh and mash in a medium bowl until smooth. Measure ½ cup mashed potato and reserve the rest for another use.

Step 2

In a stand mixer fitted with the paddle attachment, beat the butter, vanilla, and potato on medium-low speed until well combined. Reduce the speed to low and slowly add the powdered sugar, 1 cup at a time, beating until well combined and a dough forms. Stop adding powdered sugar when the dough becomes the texture of molding clay, like Play-Doh (depending on how moist the potato is, this can be between 4 to 6 cups powdered sugar).

Step 3

Place a large sheet of waxed paper or parchment paper on a work surface and lightly dust with powdered sugar. Roll out the potato candy to a 12-by-10-inch rectangle (about ¼-inch thick), dusting the top with powdered sugar if it becomes sticky. Spread the peanut butter in an even layer over the potato candy.

Step 4

Starting at one of the long sides, begin rolling the candy tightly into a log using the waxed paper as a guide, as you would roll up a jelly roll; gently peel away the waxed paper as you roll. Wrap the log in waxed paper, twisting the ends closed, and freeze until very firm, at least 45 minutes and up to 1 ½ hours.

Step 5

Place the candy log on a work surface, remove the waxed paper, and cut the candy crosswise into ¼-inch-thick slices.