Here is my recipe, got it in school in home economics in 1966.   

step 1    

Take a small peeled boil then mash well cool. Put 1 egg white in 
bowl and add potato. Beat together. Add 1 teaspoon of vanilla. Add 
confectioner sugar, until hard to stir with spoon, sprinkle sugar, on 
hands and work together. 

step 2 

Pinch off piece of candy about size of a medium potato; flatten until the size of palm of hand. 

Spread candy with Peanut butter. Roll until 10 inches long. slice in 
pieces.    Easy to do it make it. when I make mash potatoes just put 
an extra potato on then set aside to cool.    Die in Ashland,Ohio

Potato Candy; Is so simple to make, just take some leftover  mashed potatoes
add powdered sugar until the consistence is about the same as a pie crust,
roll it out, spread some peanut buter on it then roll it up then cut it into
the desired chunks.................tcw
 

 Momma's "Irish Potato Candy"
 Boil and prepare as for mashed, one large potato (use salt and butter and 
milk)
 Put in frig to get cold
Once cold, place in a very large bowl. With a wooden spoon, beat in about 1 
1/2 lbs. of powered sugar and 1 tsp. vanilla. You want the dough to be heavy 
enough that it leaves the bowl in a large ball and is impossible to stir. The 
weather will determine how much sugar to add.
Powder your bread board w/ powdered sugar.
Roll the dough out into a large rectangle, about 1/4" thick. (use pwd. sugar 
on rolling pin)
Spread one 18 oz.  jar of peanut butter over the entire surface of the dough. 
Starting at the long edge away from you, carefully roll it up like a jelly 
roll.
Let it sit for about 5 mins. With a knife, cut into 1/2" or 1/4" slices and 
lay out on a platter to air dry. Depending on the weather, it will take from 
30 to 60 mins. for it to "set". 
This candy will keep for a very long time in an air-tight container. Don't 
put in the fridge, it can collect moisture just from being cold. It won't 
last long enough to go bad.
I'm so glad so many remember this delight. I thought it would be a goner once 
i and my sisters were gone. I've tried to pass the recipe on to anyone who 
showed interest. 
With joy, Gwendolyn

Here are some variations I have found!
Potato Candy 

Recipe By : "Homemade Happiness" St.Anne's Parish, Caribou, Maine 

3/4 cup mashed potatoes -- cold 
4 cups confectioner's sugar 
4 cups coconut -- chopped 
1 1/2 teaspoons vanilla 
1/2 teaspoon salt 
4 squares baking chocolate (sweet or semisweet) 
Mix Potatoes and confectioners sugar. Stir in coconut, vanilla and salt.
Blend well. Press into one large or two small pans, so candy will be 1/2
inch thick. Melt chocolate over hot water, do not let water boil. Pour
chocolate on top of candy, cool and cut in squares. For variations, make
haystacks, by forming white mixture into cones 1 inch high. Allow to
stand uncovered for 20 minutes. Dip base of each cone in melted
chocolate. Place on waxed paper until chocolate hardens. Yields about
100 haystacks. 

Title: Irish Potato Candy
 Categories:   Christmas, Mom's best
      Yield: 16 servings
 
      1 tb Mashed potatoes                     1    12 oz jar peanut
butter
  2 1/4 c  Confectioners' sugar           
 
  Placed mashed potatoes in a mixer bowl. Add confectioners' sugar one
  cup at a time, beating well after each addition. Spread into greased
  10 x 15 inch pan. Spread peanut butter over top. Roll as for a jelly
  roll. Cut into slices.
  
  Source: Homemade for the Holidays Cookbook, 1992


similar:


 MASHED  POTATO  CANDY

 1/4 cup mashed potatoes (1 sm. potato)
 2 tbsp milk
 1 tsp vanilla
 Dash salt
 1 lb box powdered sugar
 Peanut butter

Mix together all ingredients, except peanut butter.  Add sugar until 
dough consistency. Roll out onto powdered sugar dusted bread board or 
waxed paper. Spread peanut butter all over.  Roll it up like a jelly
roll
loaf. 


and there's:


MASHED POTATO FUDGE
from: Potpourri of Cooking

1/2 Cup cooked, potatoes, mashed
2 tablespoons soft butter or margarine
1 pound confectioners' sugar
3 squares cooking chocolate, softened and melted
1 teaspoon vanilla
dash of salt

   Put mashed potatoes into a mixing bowl. Add  soft butter and mix. Add
confectioners' sugar, mix well. Add vanilla to melted chocolate, then
add
with salt to the mashed potato mix. Chill. Coconut may be added. Cut
into
bars or squares.
Place in refrigerator to chill. Slice 1/4-inch thick.

And if you are in need of any kind of potato recipe here you go:
http://www.panix.com/~donwiss/potato/


And I just had to add:
Sweet Potato Cocoons 

Recipe By : The Sweet Potato Cookbook! 

2 sticks margarine, minus 1 Tablespoon 
4 tablespoons confectioner's sugar 
2 cups sifted flour 
2 teaspoons vanilla 
1 teaspoon water 
1/2 cup sweet potatoes, mashed 
1 cup pecans -- chopped 
confectioner's sugar 
Cream margarine with sugar; add flour, vanilla, water, potatoes and
pecans. Mix well. Roll pinches of dough into small oblong rolls.
Bake on cookie sheet in 300F oven for 30 minutes. Let cool completely
and roll in confectioners' sugar.