Allow the cake to completely cool and slice it into three evenly-thick layers.
To make the soaking cream, combine milk and liqueur together. Use a spoon, pastry brush or squirt bottle to saturate each layer with the soaking cream.
Melt the semi-sweet chocolate chips in the microwave, stirring them every 10-15 seconds until silky smooth. Using a stand or hand mixer, beat the melted chocolate, softened butter, and condensed milk together until well-combined.
In a separate bowl, beat the very cold heavy whipping cream until it reaches soft peaks. Fold in the chocolatey butter mixture with a spatula.
To assemble the cake, place the first cake layer on a plate or cake stand. Spread on a layer of cake cream. Repeat until you run out of cake layers.
Using the remaining cream, decorate the outside of the cake. Dust sides of the cake with shaved chocolate. Enjoy!