For the soaking syrup: Line an 8-inch or 9-inch round springform pan with plastic wrap, allowing it to drape over the sides. Set aside.
Mix the espresso, brown sugar and rum in a bowl large enough to fit a ladyfinger, then set aside.
For the mascarpone cream: Beat the mascarpone, confectioners' sugar and salt in a stand mixer fitted with the whisk attachment on low speed to combine. Scrape the bowl and whip on medium-high until smooth. Turn the mixer on low and slowly add the heavy cream and then the vanilla and coffee liqueur. (The mixture will look like thin cheesecake batter.) Gradually raise the mixer speed to medium and whip until the cream has reached medium peaks, 1 to 2 minutes. Set aside.
To assemble: Break a ladyfinger in half and give it a quick dip in the soaking syrup, then place in the bottom of the lined pan. Repeat this process to create one layer of dipped ladyfingers. Sprinkle 1 tablespoon chopped chocolate over the ladyfingers. Spoon about a third of the mascarpone cream over the ladyfingers and spread until smooth.
Repeat the ladyfinger dipping and arranging process to create a second layer of ladyfingers over the cream. Sprinkle on the remaining tablespoon chopped chocolate. Top with the remaining cream and spread smooth. Wrap with plastic wrap and freeze for at least 8 hours, or up to overnight.
Two hours before serving, unlatch the pan and remove the tiramisu from the pan and plastic wrap to a serving platter. Sprinkle the top of the tiramisu with the cocoa powder.