Whisk the egg yolks and sugar at medium-low speed until very thick and light yellow.
Lower the speed to low and add 2 oz rum, 2 oz cup espresso, coffee liqueur, and the mascarpone. Whisk until smooth and well combined
In a separate shallow bowl, combine the remaining rum and espresso.
To build the tiramisu, I recommend you read the rest of the steps before proceeding to avoid the ladyfingers falling apart.
Have your 9x13 dish or pan nearby, along with your ladyfingers and espresso mixture.
Roll each ladyfinger, one at a time, in the espresso mixture to cover, careful not to submerge longer than 5 seconds each, or they will fall apart. Place the soaked ladyfinger in the bottom of the 9x13 pan.
Continue until half of the ladyfingers are soaked and placed in the pan.
Pour half the espresso cheese mixture over the ladyfingers and smooth out.
Continue with the rest of the ladyfingers, soaking one at a time and layering onto the cheese mixture.
Pour the rest of the cream mixture on top and smooth out.
Whisk the heavy cream until you have stiff peaks.
Carefully fold in the triple sec until just combined.
Layer the cream mixture on top and cover the dish with plastic wrap.
Place in the refrigerator for no less than 4 hours or overnight.
Before serving, sprinkle the top with shaved chocolate.