In a stand mixer with the paddle attached add the butter. Beat on high until the butter becomes pale. Push the butter down after a minute or so
Stop the mixer and add the icing sugar. Turn the mixer on LOW, until the sugar is incorporated into the butter.
Add the black cocoa and the food colouring, beat on low until incorporated.
Then add 1/2 cup milk a little at a time. Scrape down the sides of the bowl, turn the mixer on high and beat. Keep adding a tablespoon of milk at a time until your icing is a consistency you want (I used 4 tbsp).
Beat the icing on high for ten minutes. Occasionally stop the mixer and scrape down the sides of the bowl results in a very nice fluffy icing.