Preheat oven to 180 degrees C. Grease and flour one 23x23cm square pan.
Sift the flour, sugar, 3 tablespoons cocoa, baking powder, bicarb soda and salt together. Make a well in the centre and add the water, oil, vinegar and vanilla. Beat until smooth and pour batter into the prepared pan.
Bake for 30 minutes.
To make icing: Combine the 1/2 cup cocoa powder, sweetened condensed milk and butter in the top half of a double boiler and cook until thick. Spread warm mixture over the top of a slightly cooled cake.