Combine the brewed coffee, dark rum, dark chocolate liqueur, and cocoa powder in a bowl. Set aside to cool.
Heat a double boiler (or a pot with a bowl that just covers the top) with water in the bottom pot over a medium-high heat. Combine the egg yolks, sugar, salt, and 2 tablespoons of heavy cream in the top pot (or bowl). Place over the pot with the boiling water and whisk constantly, until the mixture is warmed to 160°F. Set aside and allow to cool.
Whip the heavy cream and vanilla extract in a bowl of a stand mixer until you achieve stiff peaks. Set aside. Once the egg yolk mixture has cooled, whisk in the mascarpone cheese until smooth. Fold in the whipped heavy cream.
To assemble the tiramisu, dip the ladyfingers in the coffee mixture and let sit for 3 to 5 seconds. Line the bottom of a baking dish with the coffee infused ladyfingers, but do not stack them.
Spread half of the mascarpone filling on top. Add another layer of coffee infused ladyfingers on top of that mixture. Top with the remaining mascarpone filling.
Dust the top generously with cocoa powder. Cover with plastic wrap and refrigerate for at least 8 hours.
Notes
The tiramisu can be stored in the refrigerator for up to 7 days.