Preheat oven to 350°F. Line a baking sheet with parchment paper.
Beat butter and sugar until light and fluffy. Add the flour(s), cocoa powder, salt and cornflakes and stir until combined. The mixture will look crumbly, but will hold shape when pressed together.
Take a tablespoon of the mixture and roll into a ball, flatten it slightly and place on the prepared baking sheet. Repeat with the remaining mixture, placing the cookies about 1" apart from each other.
Bake the cookies for 15~16 minutes or until firm. Remove onto a cooling rack and let the cookies cool completely.
Make the Icing: Combine confectioners sugar, cocoa powder and 1tbsp water until combined and forms a thick paste. Add 1tsp water at a time to make sure that the consistency is thick.
Immediately spread over the cooled cookies and place a walnut on top. Let the icing harden for a couple of minutes before eating.