Fill ice-cube trays with half of the brewed coffee and place in the freezer. In a bowl, combine the remaining brewed coffee, cocoa powder and milk and stir to dissolve the cocoa. Cover and chill.
When the ice cubes have frozen, transfer them to a kitchen towel and, using a hammer or mallet, crush the cubes. Fill 4 glasses with the crushed ice and divide the coffee-cocoa mixture evenly among them. Dust the top with cocoa powder and serve.