Prep for the recipe by setting out all cold ingredients and making the espresso. Pour the espresso into a shallow dish and add the rum. Set aside. Set out a separate 9X13 inch baking dish to layer the tiramisu.
Set a double boiler (or a small pot with a glass bowl resting over the top) on the stovetop. Add 1 inch of water to the lower section and turn the heat on medium. Add the egg yolks and sugar to the top of the double boiler. Vigorously whisk the sabayon mixture for 8-10 minutes over the heat until it is very smooth, thick, and much lighter in color. (It should look like lemon pudding.) Remove from heat and let it cool a little.
In the bowl of an electric stand mixer, whip the heavy cream into firm peaks. (Start on low speed, and gradually move to high, until the whipped cream is very thick and firm.) Remove the whipped cream from the mixer bowl and place it in another bowl.
Then scoop the sabayon egg mixture into the stand mixer bowl and add the mascarpone cheese and vanilla. Whip until very smooth. Scrape the bowl with a rubber spatula and beat again to incorporate any chunks.
Fold the whipped cream into the mascarpone mixture with a spatula. (Do not beat!) Continue to fold until the mixture is very even.
One at a time, dunk the Ladyfingers into the espresso mixture. Roll them over and remove them immediately. DO NOT let the Ladyfingers soak in the espresso; they will dissolve! Once dunked, arrange the Ladyfingers in a single layer, in the bottom of the baking dish. You should be able to fit 20-22 Ladyfingers in one layer.
Use a spatula to spread half of the mascarpone cream over the Ladyfingers in the dish. Then repeat with a second layer of Ladyfingers and a second layer of mascarpone cream. (4 layers total) Then place the tiramisu in the refrigerator, uncovered, and chill for at least 4 hours. You can chill overnight, but make sure to cover the top with plastic after the first few hours.
When ready to serve, place the cocoa powder in a sifter. Use the sifter to sprinkle a heavy even layer of cocoa powder over the top of the tiramisu. Cut and serve!
Don't have an espresso maker? You can buy espresso at a local coffee shop and refrigerate it until ready to use. Or you can use powdered "instant" espresso coffee and water to make espresso for this recipe.Vigorous Whisking.Sabayon gives the mascarpone cream its rich silky texture. You must whisk it well to create the right texture. If you've got an egg beater, this is a great time to use it!