In a medium saucepan over medium heat combine 1 cup sugar with 1 tablespoon water. Heat to between 234 and 240 degrees F (112 to 116 degrees C), or until a small amount of syrup dropped into cold water forms a soft ball that flattens when removed from the water and placed on a flat surface. Stir in egg whites and vanilla.
In a separate saucepan combine remaining 2 cups sugar, corn syrup and 1 tablespoon water; heat to 250 to 265 degrees F (121 to 129 degrees C), or until a small amount of syrup dropped into cold water forms a rigid ball. Stir this mixture into the other pan with sugar and
To the sugar mixture add nuts. Pour into a 9 x 9 inch dish and chill until firm. Cut into 1 inch squares.