Whip together egg yolks, and ¼ cup sugar until triple in volume. Transfer mixture to a large bowl. Set aside.
In a separate bowl whip heavy cream and remaining ¼ cup sugar until it creates soft peaks. Add mascarpone and whip until it combines and creates soft peaks. Gently fold the mixture into the egg mixture until combined.
Combine Rum and espresso in a mug and set aside
Dust the bottom of a 8x8 pan with cocoa powder
Quickly dip the lady fingers into the mug of espresso and cocoa. DO NOT SOAK or else they will fall apart. Then lay the lady fingers in the pan lined up next to each other.
Once you have a full layer of lady fingers on the bottom of the pan, spread ½ the mascarpone mixture on top forming a thick layer. Repeat a layer of lady fingers on top of that, then the rest of the mascarpone spread.
Dust with a layer of cocoa powder and shaved chocolate. Refrigerate for 4-8 hours. Serve chilled.