In a large bowl using a electric mixer with the whisk attachment, beat eggs yolks and sugar on high until thick, pale, light and fluffy. About 10 minutes. Add mascarpone cheese and blend on low speed for about 5 minutes. Add rum, blend on low for another 2-3 minutes until the rum is incorporated into the mixture.
In a 1/2 sheet pan spread a 1/2 inch thick layer of the mascarpone cheese mixture. Dip lady fingers in espresso for about 4 seconds. Layer the soaked lady finger over the cheese mixture then repeat step 1 and 2 again. Cover and refrigerate for at least two hours. Before serving grate chocolate shavings over the top.