Preheat the oven to 180˚C (160˚C for fan assisted ovens)/ Gas Mark 4.
Mix the eggs, oil, water, cocoa powder and cake mix gently together and whisk (by hand or electric mixer) for 2-3 minutes until smooth and creamy. Fold through the chocolate chips and milk.
Pour the cake mixture evenly into the two greased cake tins.
Bake in the centre of the oven for 25-28 minutes, or until a skewer inserted into the centre of the cake comes out clean. Leave the cakes in the tins for 2-3 minutes then turn out onto a wire rack and leave to cool.
Using ½ the coffee icing, spread over the top of one of the cakes, place the second cake on top then spread a thin layer around the sides of the cake. Chill in the fridge for 15 minutes.
To create the layered icing effect around the side of the cake, spread the chocolate icing all around the bottom half then start incorporating some of the coffee icing to cover the top half. Allow the two icings to merge slightly to give a two-tone effect.
Spread the rest of the coffee icing over the top of the cake and make deep circular swirls with the back of a teaspoon. Scatter over the grated chocolate.