In a medium bowl, whisk together the confectioners’ sugar and flour.
In a separate bowl, beat the whole eggs and egg yolks, then stir them into the dry to form a thick, smooth paste.
In a saucepan, scald the milk by heating it until just before it boils. Very slowly, pour the hot milk into the egg paste while whisking constantly to temper the eggs.
Pour the entire mixture back into the saucepan.
Cook over a low flame, whisking constantly, until it begins to simmer.
Continue to whisk over the lowest heat for 3 more minutes until thickened.
Remove the custard from the heat.
Stir in the butter, vanilla, and 1 tablespoon (15 ml / 0.5 fl oz) of the brandy.
Beat again until perfectly smooth.
Allow the custard to cool completely, stirring it occasionally to prevent a skin from forming on top.
In a small bowl or measuring cup, combine the cold espresso and the remaining ½ cup of brandy.
Using a long serrated knife, carefully slice the Genoese sponge horizontally into two even layers.
Place the bottom layer on a 9-inch cake platter or the false bottom of a springform pan.
Evenly spoon ⅓ of the espresso-brandy mixture over the bottom cake layer.
Spread the cooled custard evenly over the moistened cake layer.
Gently place the top cake layer over the custard. Slowly and carefully spoon the remaining espresso-brandy mixture over the top, allowing it to soak in without running down the sides.
Place the sweet cocoa in a fine-mesh sieve and sift a thick, even layer over the entire top of the cake.
Chill the cake for at least 4 hours, or preferably overnight, before serving.
Serve with fresh, hot espresso.
Stir the custard occasionally as it cools to prevent a skin from forming on the surface, ensuring a silky-smooth texture.
