Line a loaf pan that the pound cake fits in with overhanging plastic wrap.
Cut the pound cake horizontally into 4 slices. Stir the ground espresso together with the grated chocolate in a small bowl.
Place the first slice of cake in the prepared loaf pan. Drizzle the cake with 2 1/2 tablespoons liqueur. Spread half of the coffee ice cream over the cake and top with 2 tablespoons of the chocolate and espresso mixture.
Repeat the process above, this time using the chocolate ice cream. Then again, using the remaining coffee ice cream. Repeat one final time, using the vanilla ice cream and garnishing the top with the remaining chocolate and espresso mixture.
Loosely cover the cake with the overhanging wrap. Place the cake in the freezer until hardened, about 4 hours.
Remove from the freezer and unfold the plastic wrap from the top. Remove the cake form the pan and peel off the remaining plastic wrap. Slice and serve.