Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
For the chocolate cake layer, whisk together the flour, sugar, cocoa powder, baking soda, and salt in a large bowl.
Add the egg, buttermilk, oil, and vanilla extract to the dry ingredients and mix until combined.
Stir in the boiling water until the batter is smooth.
Pour the batter into the prepared pan and bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool for 10 minutes in the pan, then transfer to a wire rack to cool completely.
With a long serrated knife, cut the cake horizontally into 2 halves. Transfer one half of the cake to an 8 inch springform pan and press down to make the cake spread to the edges. (The remaining cake half can be wrapped in plastic wrap and stored for another use)
For the cheesecake layer, melt the dark chocolate chips and let cool slightly. In a separate bowl, beat the cream cheese with sugar until smooth. Add the eggs one at a time, then the vanilla extract. Fold in the cooled chocolate.
Pour the cheesecake mixture over the cooled cake layer and bake for 40-45 minutes, or until set. Cool to room temperature, then refrigerate until firm.
For the custard layer, whip the heavy cream to stiff peaks. In another bowl, blend the mascarpone cheese with powdered sugar and vanilla extract until smooth. Gently fold in the whipped cream and spread the mixture over the cheesecake layer. Chill in the refrigerator.
For the icing, heat the heavy cream for the dark chocolate until it begins to simmer, then pour over the dark chocolate chips and stir until smooth. Repeat with the white chocolate chips and remaining cream. Drizzle both dark and white chocolate icings over the custard layer. Use a toothpick to create a swirl pattern.
Press mini chocolate chips around the sides of the cake.
Chill the cake for at least 2 more hours before serving.
Instructions for Making and Applying the Ganache Frosting:
Place the chocolate chips in a medium heatproof bowl.
Heat the heavy cream in a small saucepan over medium heat until it just begins to simmer.
Pour the hot cream over the chocolate chips and let it sit for about 4-5 minutes to melt the chocolate.
Stir the mixture until the chocolate is fully melted and the ganache is smooth.Let the ganache cool until it reaches a spreadable consistency, stirring occasionally. (about 2 hours at room temperature, or 1 hour in the refrigerator)
Use an electric mixer to beat the ganache frosting. Transfer to a piping bag fitted with a star tip and pipe around the top edge of the cake. Slice cake and enjoy!