In a pie dish or shallow bowl, combine the coffee with 1/4 cup rum, and set aside.
Whisk together the yolks, sugar and salt in the top of a double boiler (or in a stainless steel bowl set over a pot of simmering water). With the heat set to low, stir almost constantly with the whisk, until the temperature of the yolks reaches 160 degrees F, 10-15 minutes. (See recipe notes; you can skip this step if you purchase pasteurized eggs).
Remove from the heat and pour the yolk mixture into a stand mixer fitted with the whisk attachment (or use a large, clean bowl and an electric mixer). Beat until pale, thick and creamy, approximately 4 minutes. Add the mascarpone cheese and remaining rum. Mix on medium speed to incorporate the ingredients, which will look lumpy. Turn off the machine, scrape down the sides of the bowl, and turn the speed up to high for 3 minutes, until thick and very smooth.
Using a stand mixer with the whisk attachment or an electric mixer, beat the heavy cream to a stiff peak (this can also be done by hand with a bowl and whisk). Fold the whipped cream into the yolk mixture.
Grab the pie dish with the coffee, and place it next to a 9x13 dish (standard baking dish, glass, ceramic, etc).
Very briefly dip the ladyfingers into the coffee, then line them along the bottom of the pan (my pan held exactly 24 per layer). Do not flip the ladyfinger in the liquid to coat the other side evenly, and do not hold it in the liquid. Too much liquid = mushy dessert that seeps coffee.
Once you have a single layer, top with half of the custard mixture, spreading evenly with a spatula. Sprinkle evenly with half of the grated chocolate. Repeat with the remaining ladyfingers, custard, and chocolate. If desired, sift a light coating of cocoa powder on top of the bittersweet chocolate to fill in any chocolate gaps (this is more about presentation than flavor).
Cover the pan tightly and refrigerator for a minimum of 4 hours or overnight.
To serve, scoop into individual bowls or onto plates.
Pasteurized eggs can be difficult to locate in stores, but if you can find them, you can skip the step of cooking the yolk mixture to 160 degrees and place it directly in the mixer.
If you don’t drink alcohol, you can omit it from the recipe. I would add an additional 1/4 cup heavy cream to make up for some of the lost volume.
In my opinion, this has a perfect balance between custard and ladyfingers. However, some versions of tiramisu have thicker custard layers. If you want thicker custard layers, you can increase the custard ingredients by 1/2 or even double. This will increase the time required to heat the yolks to 160 degrees, as well as possibly the time required in the stand mixer (only by a minute or two).