Preheat oven to 350°F (175°C).

Grease an 8-inch springform pan.

In a food processor, pulse chocolate brownies and 1/3 cup chocolate chips until fine crumbs form.

Press the brownie mixture into the base of the prepared pan.

Bake the crust for 15 minutes.

Let the crust cool completely.

Gently melt the remaining chocolate chips in a heatproof bowl set over a saucepan of simmering water, stirring occasionally until smooth.

Let the melted chocolate cool to room temperature.

In a small bowl, whisk together espresso powder dissolved in hot water, heavy cream, coffee liqueur, and vanilla extract.

Set the coffee cream mixture aside.

Reduce oven temperature to 325°F (160°C).

Place a baking pan filled with 2 cups of water on the lowest oven rack to create a water bath.

In a food processor, combine cream cheese, granulated sugar, cocoa powder, and melted chocolate.

Puree the mixture until smooth.

Add eggs and egg yolk to the cream cheese mixture.

Puree until smooth.

Add the coffee cream mixture to the cream cheese mixture.

Puree until completely smooth.

Transfer the cheesecake batter to the prepared springform pan.

Bake for 1 hour and 10 minutes.

Turn the oven off and let the cheesecake cool in the oven with the door ajar for 1 hour.

Chill in the refrigerator for at least 4 hours, or preferably overnight.

To serve, spread whipped cream evenly over the top of the cheesecake.

Spoon chocolate frosting into a piping bag fitted with a small star tip.

Pipe 12 rosettes of chocolate frosting around the edge of the cheesecake.

Top each rosette with a small piece of marbled chocolate bark.