Then stir together flour, sugar, butter, eggs, cocoa powder, water and finely grated apples until you have a homogeneous mixture.
Bake the dough in a well-greased loaf pan for about 60 minutes at 160 °. Do a chopstick test to see whether it is ready (very light residues are ok, as it is a very moist cake).
Let the cake cool down and remove it from the mold.
Now heat the powdered sugar, cocoa powder, butter and milk in a water bath until you have a homogeneous, spreadable mixture. If the mixture is too firm, just add a little more milk.
Spread this mixture on the cooled cake and let it cool down.