Prepare a 9 x 13 inch cake as directed on the label of the cake mix box.
Bake and let it cool slightly in the pan. Invert onto a rack to cool completely.
Cleaning out the used cake pan, line it with plastic wrap.
Cut the cake in half lengthwise, and then in thirds crosswise, making 6 rectangles.
Slice each rectangle in half to make two layers, using a serrated knife.
Arrange half of the pieces snugly in the cake pan.
Crumble the remaining pieces and press tightly into 6 small balls.
Arrange 1 cake ball in the center of each cake rectangle in the pan.
To make the mousse: In a heatproof bowl set over a saucepan of simmering water, heat the chocolate, butter, coffee and ¼ cup water. Do not let the bowl touch the water. Stir often, until melted.
After removing the bowl from the pan, stir until cooled off.
Reserve the simmering water.
Fill a large bowl with ice water.
Mix the egg yolks, 1 ½ cups sugar and 2 tablespoons water in a separate large heatproof bowl, using a whisk.
Place this bowl over the saucepan of simmering water, whisking for 6 to 8 minutes, or until pale yellow.
Pour in the chocolate-coffee mixture and the vanilla. Mix with a whisk about 2 minutes, or until combined.
Remove the bowl from the pan and set in the bowl of ice water.
Whisk for about 4 minutes or until slightly cool but not thick.
Using a mixer, beat the egg whites and salt in a bowl until foamy.
Adding 2 tablespoons of sugar, beat until almost stiff.
Gently fold into the chocolate-yolk mixture to make a dark chocolate mousse.
Spread 5 cups over the cake and cake balls.
Freeze for about 30 minutes or until firm on top.
Beat the heavy cream and the remaining 4 tablespoons sugar until soft peaks form.
Fold this mixture into the remaining mousse.
Remove the cake from the freezer.
Spread with the light chocolate mousse.
Cover with plastic wrap and freeze at least 6 hours or overnight, until firm.
To make the chocolate shell- In a heatproof bowl set over a saucepan of simmering water, stir the chocolate, heavy cream and 4 tablespoons corn syrup, until melted. Do not let the bowl touch the water. Spread half of the shell mixture over the frozen mousse, a spoonful at a time. Return to the freezer.
To make the chocolate sauce - Add the remaining 1 tablespoon corn syrup and the butter to the remaining chocolate shell mixture. Put in microwave 30 seconds. Stir until glossy.
For serving the cake, beat the heavy cream with a mixer until foamy. Add the sugar and beat until soft peaks form. Remove the cake from the freezer. Invert it onto a baking sheet and unmold. Invert again onto a platter, with the chocolate shell-side up.
Using a warm knife, cut the cake in half lengthwise. Then cut into thirds crosswise to make 6 rectangles. Cut each rectangle in half diagonally to make 2 triangles.
Top each triangle with whipped cream, ice cream and the prepared chocolate sauce.