Preheat oven to 350 degrees F (175 degrees C). Grease two 9-inch cake pans and dust with 1 tablespoon cocoa.

In a heavy saucepan over low heat, combine 1 1/4 cups butter, 1 cup stout beer, 4 ounces dark chocolate, and superfine sugar. Heat, stirring occasionally, until chocolate is melted and smooth. Remove saucepan from heat and cool slightly.

Beat eggs and creme fraiche together in a large mixing bowl; gradually stir in the flour and baking soda. Add the melted chocolate mixture in small additions, beating well after each addition. Pour half the batter into each prepared cake pan.

Bake in the preheated oven until the top of the cake bounces back when touched lightly with a finger, about 40 minutes. Cool the cakes on racks.

To make the icing, place 1/2 cup butter, 4 ounces dark chocolate, and 5 tablespoons stout beer in a heavy saucepan over low heat. Cook, stirring occasionally, until the chocolate has melted. Remove from heat and cool slightly.

In a mixing bowl, blend cream cheese, 1/3 cup cocoa powder, and vanilla extract until combined. Stir in 1/2 cup confectioners' sugar. Pour in the cooled chocolate-stout mixture and beat well. Gradually add remaining confectioners' sugar until icing reaches the desired thickness.

Place 1 cake on a serving plate and smooth about 1/3 of the icing over the top. Place the second cake onto the frosted layer, and spread remaining 2/3 of the icing over the top and sides of the cake.