1 cup mashed potatoes, room temperature or cold
1/2 cup (1 stick) unsalted butter, room temperature
1 teaspoon vanilla extract
3 pounds confectioners sugar
1/2 cup smooth peanut butter, divided
In a large mixing bowl, stir together mashed potatoes, butter, and vanilla. Add confectioners sugar, one pound at a time, and stir together well. The dough will be very wet, but it will come together into a more firm dough after you incorporate the last pound of confectioners sugar. Once the dough is thoroughly mixed, divide it into two halves.
On a sheet of wax paper, and using your hands, flatten out one of the halves of dough into a rectangle. Cover the dough with a second sheet of wax paper and, using a rolling pin, roll the dough until it is roughly 13-14 inches long and 10 inches wide. Lift the wax paper and dough carefully, place on a baking sheet, and chill for about 5-10 minutes only. Remove from refrigerator and spread 1/4 cup peanut butter evenly onto the dough. From the long side, carefully roll into a log and wrap well in wax paper. Repeat with other half of dough. Chill the logs for at least 2 hours before slicing. Once chilled, slice into 1/2-inch pieces and serve.
Make ahead: Store prepared potato candy, layered between sheets of wax paper, in the refrigerator in a covered container for up to 2 weeks.