In a medium bowl, heat the chopped chocolate in the microwave on high in 15-second increments, stirring occasionally, until melted and smooth. Let cool 10 minutes.
In a medium bowl using a rubber spatula, stir the butter vigorously until smooth. Add 1 cup sugar and stir vigorously to blend. Separate the eggs; place the yolks and whites into 2 separate medium bowls. Whisk the yolks just to blend. Using a whisk or an electric mixer, beat the whites just until soft peaks form. Fold the yolks into the whites. Fold the egg mixture into the butter mixture until just blended. Fold in the melted chocolate (the frosting will still be slightly grainy).
In a wide, shallow bowl, stir the espresso and the remaining 2 tbsp. sugar until the sugar dissolves. Place 1 cookie in the espresso; let soak 3 seconds. Flip cookie over; let soak 3 more seconds. Transfer to a rectangular plate or platter. Repeat with 7 more cookies, arranging the cookies in a rectangle 2 cookies wide and 4 cookies long.
Spread 1/2 cup of the frosting on the cookies, leaving the scalloped edges exposed. Repeat four more times with the remaining cookies, espresso mixture and frosting to make a five-layer cake. Top with the chocolate curls. Refrigerate until the cookies soften, at least 3 hours.