Remove the pound cake from its pan and line the pan with plastic wrap, leaving plenty of overhang. Slice the pound cake horizontally into 3 slices.
Mix the hot coffee with the brown sugar in a small bowl until the sugar has dissolved. Set aside.
Add the cream cheese, powdered sugar and vanilla bean paste to a large bowl. With a hand mixer, beat the mixture until smooth. Add the heavy cream and continue to beat until stiff peaks form. Transfer to a piping bag fitted with a wide tip and set aside.
To build, place one layer of cake in the bottom of the lined pan and press. Spoon over a third of the sweetened coffee, allowing it to soak in. Pipe a third of the cream mixture over the cake. Grate over a third of the chocolate. Repeat the process 2 more times, ending with the grated chocolate. Loosely cover with the overhanging plastic wrap and chill for 4 hours.
Carefully lift the cake from the pan and remove the plastic wrap. Slice and serve.
