Step 1

In a shallow bowl, mix the boiling water, instant espresso, and ¼ cup of the rum. Set aside and allow to cool to room temperature.

Step 2

In the bowl of an electric mixer fitted with the whisk attachment or beaters, beat the egg yolks with the salt and ⅔ cup of the sugar on medium speed until the mixture is thick, pale yellow, and forms a ribbon when the whisk is lifted out of the bowl, about 2 minutes. Add the mascarpone, vanilla, and remaining ¼ cup of rum and beat until the mixture is smooth, about 1 minute.

Step 3

Using another bowl for your electric mixer fitted with the whisk attachment or beaters, beat the heavy whipping cream and remaining ⅓ cup sugar on medium speed until medium-stiff peaks form, 1½ to 2 minutes. Be sure not to over whip the cream; otherwise it will curdle.

Step 4

Using a rubber spatula, fold about ½ cup of the egg-mascarpone mixture into the whipped cream just until combined. Add the remaining egg-mascarpone mixture into the whipped cream and fold about 20 times, or until the mixture is uniform (no streaks should remain). Set aside.

Step 5

Set up a workstation with the ladyfingers, the cooled coffee mixture, and a 9x13-inch ceramic or glass baking dish.

Step 6

One at a time, dip the ladyfingers into the coffee mixture for 2 to 3 seconds each (do not oversaturate the cookies or they will fall apart), and place into the pan. Arrange the dipped cookies in a single layer in the baking dish (about 20 cookies), breaking or trimming them as needed to fit neatly into the dish.

Step 7

Spread half of the mascarpone mixture over top of the ladyfingers and, using a spatula, smooth into an even layer. Using a small sieve, dust the top of the cream layer with 1 tablespoon of the cocoa powder. Repeat with another layer of soaked ladyfingers, then top with the remaining mascarpone mixture and dust with the remaining 1 tablespoon cocoa powder.

Step 8

Cover the pan with plastic wrap and leave in the fridge for at least 8 hours but preferably 24 hours. Cut into squares and serve cold.