I have seen this candy made with and without mashed potatoes. My husband didn't believe me when I said my grandmother used to make peanut butter candy from mashed potatoes! Here is the recipe I use today (it is without potatoes).

1 stick real butter - soft at room temperature
1 box 10X sugar
1 small can evaporate milk
1 Jar Jiff smooth peanut butter

With a wooden spoon mix together the softened butter and the whole box of powdered sugar. Next add a little of the canned milk, only enough to make a nice dough for rolling. Do not get dough too wet! You can also add a few drops of vanilla if desired at this point. Divide the mixture into two balls. Roll out each ball on waxed paper so that it forms a rectangle. Spread with a thick layer of peanut butter. Roll up using the waxed paper to help you so that it forms a long roll. Wrap the waxed paper around each roll and put in the fridge for about 2 - 3 hours until very firm. Cut into 1/2 inch slices with a sharp knife and enjoy! Hope this helps. Hope in VA