In a shallow bowl, combine coffee and 2 tablespoons of rum.
In a medium heatproof bowl, add egg yolks, 2 tablespoons rum, 1/4 cup of sugar, and vanilla extract.
Place this bowl over a saucepan with about 1-inch of simmering water. This method is known as a double boiler. Just make sure the bottom of your bowl doesn’t touch the water!
Whisk the egg mixture vigorously until it becomes light, foamy, and triples in volume, about 5 minutes.
Incorporate the mascarpone cheese into the egg mixture and whisk until smooth.
In a separate bowl, whisk the heavy cream and remaining 1/4 cup sugar until medium peaks form.
Gently fold in 1/3 of the whipped cream into the mascarpone mixture. Then, fold in the remaining whipped cream until it is just combined.
Quickly dip enough ladyfingers in the coffee mixture, just about 2 seconds per side, to cover the bottom of an 8-inch square dish.
Spread half of the mascarpone mixture evenly over the dipped ladyfingers.
Next, dip the remaining ladyfingers in coffee and arrange them on top of the cheese mixture.
Spread the rest of the mascarpone cheese over the ladyfingers in an even layer.
Finally, sprinkle cocoa powder evenly over the tiramisu. Clean the edges of the dish, cover with foil, and refrigerate for at least 8 hours or up to 2 days.
Allow the tiramisu to sit at room temperature for 20 minutes before cutting. Sprinkle with more cocoa powder just before serving.