Lightly grease a 9-inch springform pan with butter. Then line the bottom of the pan with a circle of parchment paper.
Use a food processor and pulse the ladyfingers until they are finely ground.
Mix the ladyfinger crumbs with the melted butter and rum in a medium bowl.
Pour the ladyfinger mixture into the prepared springform pan. Then use the bottom of a glass or your fingers to press the crumbs into the bottom to form the crust.
Bake the crust for 6 minutes. Then let cool completely while you make the filling.
Make the cheesecake:
Lower the oven temperature to 325°F (163°C).
Whip the room-temperature cream cheese, mascarpone, and sugar together with an electric mixer on medium speed for about 3 minutes or until very smooth. There should be no lumps in the mixture.
Whip in the flour and espresso powder at medium speed until well combined.
Whisk the room-temperature whole eggs and egg yolks together in a bowl. Now, add half of the eggs to the cheese mixture and mix on low speed until fully combined. Then repeat the process with the other half of the eggs.
Mix in the sour cream and vanilla on low speed. Use a rubber spatula to scrape down the sides of the bowl as needed to ensure that the batter is well combined.
Pour the cheesecake batter on top of the cooled crust, making sure to spread it evenly.
Tightly wrap the bottom and edges of the springform pan with a piece of aluminum foil. Then place the foil-wrapped pan into a large roasting pan. Now, fill the roasting pan with about half an inch of hot water.
Transfer the cheesecake in the water bath to the preheated oven and bake it for about 80 to 90 minutes. When it’s done it should be fully set but the middle will still just barely jiggle.
Let the baked cheesecake cool for about 15 minutes in the water bath. Then transfer it to a wire rack to finish cooling to room temperature.
Wrap the entire cheesecake in plastic wrap and freeze it overnight still in the pan.
The following day, remove the cheesecake from the freezer and release it from the springform pan. You may need to first let it out for a few minutes.
Place the cheesecake on a serving platter. Then put it in the fridge and give it about 3 to 4 hours to finish thawing out.
Make the topping:
When ready to serve, use an electric mixer to whip the cold heavy cream and powdered sugar together until stiff peaks form. Then transfer the whipped cream into a piping bag fitted with a large round tip.
Dust the top of the cheesecake with cocoa powder.
Pipe the whipped cream around the edges of the cheesecake.
Grate semisweet chocolate on top of the cheesecake to add one last finishing touch.