In a small to medium-sized bowl, mix the cooled espresso with 1/3 cup of Kahlua and 1 tablespoon of refined sugar.  Set aside.

Separate the egg whites from the yolks into two large bowls.  Beat the egg whites until they are firm.

To make the cream filling, whisk the egg yolks until frothy then add the remaining 1/3 cup of Kahlua.  Mix well;  then add the mascarpone cheese and remaining 3 tablespoons of refined sugar.  Once fully blended, fold in the beaten egg whites.

Cover the bottom of an 8-inch square baking dish with a generous layer of cream filling.  Using half of the cookies, fully dip each ladyfinger in the espresso & Kahlua mixture and hold there for several seconds. Carefully arrange them in a single layer over the bed of cream.

Add a generous layer of cream filling to fully cover soaked ladyfingers.  Sprinkle with about half of the shredded chocolate.  Repeat with one more layer and finish off with the remaining cream filling and grated chocolate.

Cover the dish and place it in the freezer for 3 hours to set.  Transfer the dish to the refrigerator until ready to serve.