Preheat oven to 350 degrees and line a jelly roll pan with parchment paper. Grease parchment paper with butter or cooking spray.
Combine cake mix, eggs, and melted ice cream in mixing bowl and beat with mixer for one minute on low speed. Scrape down the sides of your bowl and increase speed to medium and continue mixing for another 2 minutes. Add chopped chocolate and mix in by hand.
Spread batter into prepared pan and bake for about 18-20 minutes or until golden and cake springs back when touched lightly. Let cool in pan for 5 minutes and turn out onto a wire rack. Let cool completely and cut into three sections.
To make frosting beat butter with electric mixer for 5 minutes until light an fluffy. Add sugar, about 1/2 cup at a time and beat for 5 minutes after each addition. Mix in espresso and liqueur mixture.
When making this cake for adults only, I suggest brushing the cake layers with additional coffee liqueur. Divide butter cream into three portions. Using a spatula, spread frosting evenly on cake layers, ending with a final layer of filling on top. Keep the sides unfrosted and trim the edges with a sharp knife if they don’t line up evenly. Dust the top layer with cocoa powder.