Sift the flour, baking powder, and cocoa into a bowl and add the butter, sugar, eggs, and coffee. Beat well, by hand or mixer until smooth. Then spoon into a greased and floured shallow 11x7 inch pan and smooth the top.
Bake in a 350 degree preheated oven for 35 to 40 minutes, or until risen and firm, then turn out onto a wire rack to cool completely. To make the frosting, place the chocolate, butter and mlk in a bowl and set over a pan of simmering water and stir until the chocolate has melted.
Remove the bowl from the pan and sift in the confectioners' sugar. Beat until smooth, then spread over the cake. Dust the top of the cake with sifted cocoa. Cut into 20 squares.