Yield: 3 dozen pieces.
1 large russet potato
1 tablespoon milk
1 teaspoon vanilla extract
⅛ teaspoon salt
6-7 cups powdered sugar, plus more for dusting and rolling
⅓ cup creamy peanut butter
Peel and dice the potato. Simmer in a saucepan of lightly salted water until tender, about 15 minutes. Drain well. In a large bowl, mash with a fork or potato masher until smooth. Measure out ⅓ cup of the potato puree. Discard the rest or save for another use. Set the puree aside to cool to room temperature.
Add the milk, vanilla, and salt, and mix with an electric mixer set to medium speed until very smooth, about 2 minutes.
Beat in 6 cups of the powdered sugar, 1 cup at a time, to form dough the consistency of modeling clay. If the dough is too soft, continue beating in powdered sugar, 1 tablespoon at a time. Gather the dough into a ball and dust with powdered sugar.
Dust a large sheet of parchment paper with powdered sugar. Roll the dough into a 10-by-12-inch rectangle about ⅛ inch thick. Trim the edges to make them straight. Generously sprinkle powdered sugar over the dough. Place a second sheet of parchment paper over the dough. Flip over the dough and discard the sheet of parchment that’s now on top.
Spread the peanut butter evenly over the dough. Starting at one long side, tightly roll up the dough (jelly-roll style), using the parchment paper as a guide. Wrap the roll in the parchment paper and freeze for 1 hour.
Using a sharp knife and a gentle sawing motion to avoid crushing or flattening the roll, cut it into ¼-inch-thick slices. Store the candy in an airtight container in the refrigerator for up to one week.