Lightly grease and flour the base of a 9-inch round springform pan. Break the chocolate into small pieces and place in a small pan with the butter. Have the heat turned low and stirr until melted and well combined.
Place half of the finely granulated sugar (2 1/4 ounces) in a bowl with the egg yolks and beat until the mixture is pale and creamy. Add the melted chocolate mixture, beating until well combined.
Sift the cream of tartar and the flour together and fold into the chocolate mixture, along with the ground almonds and the almond extract.
Beat the egg whites in a seperate bowl with an electric beater until light and foamy, making soft peaks. Add the rest of the finely granulated sugar and use the electric beater for about a minute, no more, until thick and glossy. Carefully fold the egg whites into the chocolate mixture and spoon into the pan. Bake in preheated oven at 375 degrees fahrenheit for 40 minutes, until it is springy to touch. Check five minutes ahead of time to avoid burning.
Heat the Icing ingredients in a double boiler. Remove from heat and beat by hand for 2 minutes. Chill in fridge for 30 minutes. Transfer cake to a plate and spread with the icing. Scatter the slivered almonds and drizzle the melted chocolate back and forth.