Place the cooled mashed potato into a large bowl. Add the butter and beat with an electric hand mixer until smooth.
Add the vanilla and salt, stir in until combined.
Start adding in the powdered sugar 1 cup at a time, fully mixing in the first cup before adding the next. How much you use depends on how watery your potato is and humidity, etc. You want the consistency to be like cookie dough that you can roll out. When you put a little bit in your fingers you should be able to press and mold it together.
In this step, you have to work pretty quickly because it can dry out. Layout a large piece of wax or parchment paper, dust it generously with powdered sugar. Place the potato mixture on the paper, add a generous amount of powdered sugar on top. Roll it out to ¼ inch thick. Try to get this into a rectangle shape as well as you can.
Smear the peanut butter all over the top leaving a half-inch border.
Tightly roll into a long log. Place on a piece of plastic wrap and roll the log up and tuck the ends under. Place in the fridge for 10 minutes to set.
Unwrap on a cutting board and cut into ¼-½ inch slices to serve.
Notes
Use real potatoes not mashed.
Russet potatoes are the best for this recipe.
You can make your potatoes how you'd like but we microwave ours.
Try different butters to switch up the flavors.
This can be frozen, see my tips above.
This can be made a day in advance and stored in the refrigerator.
To get clean cuts, wipe your knife off after each cut.