Prepare your hot cocoa just as directed earlier, but use water in place of milk and increase the cocoa powder to one and a half times the usual amount for drinking. Set it aside to cool while you continue with the rest. Once it is just warm to the touch, stir in the vanilla and rum extract. Since the mixture is quite rich in cocoa, give it a good whisk now and then so it stays smooth and well blended.

Place a medium saucepan on the stove with about 2 to 5 cm, 1 to 2 inches, of water and bring it to a gentle simmer. Meanwhile, in a heatproof bowl that can sit over the pan, whisk the egg yolks on low speed until they come together. Add the sugar and salt, then increase the speed and beat until the mixture turns pale and slightly thickened, about 1½ to 2 minutes, scraping the sides once or twice. Pour in ¼ cup of cream and mix briefly until combined.

Set the bowl over the simmering water, making sure it does not touch the surface. Stir continuously with a heatproof spatula, working along the bottom and sides, until the mixture thickens enough to coat the back of a spoon. This will take about 4 to 7 minutes. Remove from the heat and stir briskly for a moment to release excess heat, then let it cool to room temperature, about 15 minutes.

Once cooled, add the mascarpone and beat until the mixture is smooth and free of lumps. Transfer this to a larger bowl. In the same mixing bowl, whip the remaining ½ cup of heavy cream until it holds firm peaks. Fold one third of the whipped cream into the mascarpone mixture to lighten it, then gently fold in the rest until the cream is fully incorporated and silky. Set aside.

Give your cocoa mixture another thorough whisk and pour it into a shallow dish. Dip each ladyfinger briefly, about 1 to 2 seconds per side, just enough to moisten without making them soggy. Arrange them snugly in an 8-inch square dish to form the first layer, trimming if needed to fit.

Spread half of the mascarpone cream evenly over the biscuits, reaching all the way to the edges. Lightly dust with half of the cocoa powder using a fine sieve.

Repeat with a second layer of dipped ladyfingers, then cover with the remaining mascarpone cream, smoothing the top. Finish with the last dusting of cocoa powder.

Refrigerate for at least 4 hours so the dessert can set properly, though it may be prepared a day ahead if you like. When ready to serve, slice into neat squares and bring it to the table.