Cake: Preheat oven to 180 degrees C. Grease and line a shallow rectangular tin (25x20cm).
Sift the flour, baking powder and cocoa into a bowl and mix. Add the caster sugar, beaten eggs, softened butter and coffee mixture. Mix well by hand or with electric beater until smooth. Spoon the mixture into the tin and smooth out the top. Bake in preheated oven for 40 minutes or until firm and springy. Leave to cool in the tin for 10 minutes then tip out on to a wire rack and remove the lining paper.
Icing: Break the white chocolate into pieces and place in a bowl with the icing sugar, butter and milk. Place in the microwave on medium heat for 30 seconds or until the chocolate has melted and the mixture is smooth.
Spread icing over cake then dust with cocoa powder, if desired. Cut into squares to serve.