Make the cream layer. In a large bowl add egg yolks and ¼ cup of sugar. Beat with an electric mixer until mixture triples in volume, and is very pale. A ribbon of batter should fall from beaters when lifters. Set aside.
In a medium-sized bowl, add heavy cream and remaining ¼ cup of sugar. Beat with an electric mixer until soft peaks form. Add the mascarpone and beat until medium peaks form.
Gently fold the cream mixture into the egg yolk mixture, until fully incorporated and no streaks remain. Set aside.
Set up your assembly station. Grab a shallow bowl and combine espresso and rum. Sift cocoa powder to coat the bottom of a 2-quart baking dish.
Working one at a time, quickly dip each ladyfinger into the espresso mixture, being sure to coat the outside but not letting it sit and become too soggy. Place them rounded side up, side-by-side along the bottom of the dish, breaking the ladyfingers as needed to fill in the space.
Spread half of the mascarpone cream mixture over the ladyfingers in an even layer. Repeat the next 2 layers with the remaining ladyfingers and cream.
Dust the top layer with remaining cocoa powder and chocolate shavings. Cover with plastic wrap and refrigerate for at least 4 hours (overnight is better so the flavors really meld together).
When ready to serve, slice and serve onto a plate and enjoy!