Add the egg yolks and half of the sugar to a bowl. Mix on high until it becomes silky, thick, and a light golden color. Set aside.
In a separate bowl add the mascarpone cheese, heavy cream, and remaining sugar. Mix until it becomes thick and fluffy.
Add some of the egg yolk mixture into the mascarpone mixture and fold to combine. Add the remaining egg yolk mixture and fold until it's just combined.
Sprinkle 1 tablespoon of cocoa powder into the baking dish and spread it around.
Dip half of the lady fingers, one at a time, into the cold brew coffee rum, careful not to over soak them. Lay them out into the bottom of the pan.
Spread half of the mascarpone mixture over the lady fingers. Spread it out until even.
Dust the top with cocoa powder. Dip the remaining lady fingers in the cold brew coffee rum. Lay them on top of the mascarpone layer.
Spread the other half of the mascarpone on top. Sprinkle with the remaining cocoa powder.