Dust a clean dishcloth thoroughly with confectioners' sugar.
Bring white sugar, water, and corn syrup to a boil in a saucepan. Do not stir once syrup begins to boil. Heat to 240 degrees F (115 degrees C) or until a small amount of syrup dropped into cold water forms a soft ball that flattens when removed from water and placed on a flat surface.
Beat egg whites in a glass, metal, or ceramic bowl on low speed until soft peaks form, about 5 minutes. With mixer running, gradually pour hot syrup mixture into egg whites as they beat. Once all the syrup has been added, increase the speed to medium and beat until egg whites are thick, stiff and no longer glossy. The sides of the bowl should be cool to the touch.
Dust rolling pin lightly with confectioners' sugar. Roll out egg white mixture on the dishcloth to a rectangle about 3/16-inch thick. Spread peanut butter evenly on top.
Roll candy carefully into a log and let cool. Slice into pieces about 1/2-inch thick.