Make mashed potatoes by peeling, cubing, and boiling the potatoes until fork tender. Drain, mash, and cool the potatoes to room temperature.
Combine the cooled mashed potatoes with softened butter, vanilla, and 1 cup of powdered sugar. Use a hand mixer to mix well, then add the powdered sugar 1 cup at a time, mixing well after each addition, until you reach 6 cups. The dough should be firm and moldable, like play-dough. If necessary, add additional powdered sugar until you reach this consistency.
Transfer the mixture to a sheet of wax paper dusted with powdered sugar. Dust the top of the dough and/or rolling pin as well to prevent sticking. Working quickly to keep the dough from drying out, roll the mixture into a rectangle (or as close as possible) 1/4 inch thick. Add the peanut butter and spread it evenly over the top, leaving about 1/2 inch border around the edges.
Roll the dough tightly, lengthwise, into a log. Wrap in wax paper and refrigerate, seam side down, for at least 15 minutes to allow the peanut butter to "set". Note: feel free to refrigerate longer. 15 minutes is just the minimum.
Once you're ready to serve it, remove the roll from the refrigerator, unwrap it, and slice it into pieces 1/4 inch thick. Place on a serving plate and enjoy!
Store leftover candy in an airtight container in the refrigerator for up to 10 days.