Preheat the oven to 350 degrees F. Butter and flour the sides of 2 (8-inch) cake, or sandwich pans, and line the bases with grease proof or parchment paper.
In a bowl sitting over a saucepan of gently simmering water, not touching the bottom of the bowl, stir the chocolate and the milk together until the chocolate has melted.
Beat the 10 tablespoons butter until very soft, and then add the sugar and continue to beat until the mixture is light and fluffy. Beat in the eggs, 1 at a time, and then fold in the melted chocolate.
Sift in the 7 ounces flour, cocoa powder, baking powder and the baking soda, and fold in gently to mix. Divide the mixture evenly between the 2 pans, and bake in the oven until a skewer inserted into the middle of each cake comes out clean, about 25 minutes.
Remove the cakes from the oven and let sit for a few minutes before turning them out of their pans, and placing them on a wire rack to cool.
To make the chocolate butter icing: Beat the butter, cream and the vanilla extract until very soft. Then gradually sift in the confectioners' sugar, and the cocoa powder, beating constantly, until it is all added. Continue to beat until very soft, and then whisk the mixture until it is light and fluffy.
Once the cakes are cool, sandwich them together.
I normally make the chocolate butter icing in an electric food mixer, using the whisk attachment all the way through. I normally sandwich them together bottom to bottom - if you know what I mean!) with the chocolate butter icing. Place the cake on a plate, or on a cake stand, and dust with cocoa powder or confectioners' sugar, if you wish.