In a large mixing bowl beat butter or margarine with an electric mixer on medium speed for 30 seconds. Add sugar and salt and beat until fluffy.
Add egg and vanilla. Beat well. With mixer on low speed gradually beat in flour until well mixed.
Shape the dough into 1-inch balls. Press a piece of desired candy in center of each and shape the dough around it so you can't see the candy. Place balls about 2 inches apart on ungreased cookie sheets.
Bake in a 350 degree F oven about 15 minutes or until edges are golden. Place powdered sugar in a plastic bag. With pancake turner transfer 2 or 3 hot cookies at a time to the bag of powdered sugar. Gently shake cookies in powdered sugar until coated. Cool on a cooling rack. When cool, gently shake cookies again in powdered sugar. Makes about 36 cookies.
Store cookies in airtight container at room temperature up to 3 days.