Beat the egg yolks, castor sugar and vanilla essence together in a large heatproof bowl until thick and creamy, using a balloon whisk or an electric hand-beater.
Place the mixture in the top of a double boiler over hot water, or place the bowl containing the mixture over a medium-sized saucepan of hot water. The water should not touch the bowl, or come to the boil, otherwise the eggs will curdle (all you want to do is to cook the eggs very lightly, to take away the raw taste).
Continue beating for 3 to 5 minutes over the hot water, or until the mixture thickens and is pale cream in colour.
Remove the top of the double boiler, or the bowl, from the pan of hot water and continue beating for 1 to 2 minutes, or until the mixture has cooled slightly. Allow to cool completely.
Add the egg mixture to the mascarpone cheese in another bowl, gently lifting and folding them together until evenly blended.
Mix the coffee, coffee liqueur and brandy.
Place the sponge fingers in a dish. Spoon over some of the brandy and coffee mixture to moisten the sponge fingers, making sure that they are evenly covered and not too soggy.
Using a rubber spatula or egg lifter, transfer a layer of the moistened sponge fingers to the serving dish. Cover with a thick layer of mascarpone mixture.
Continue layering well-moistened biscuits with mascarpone mixture, ending with a layer of mascarpone mixture. (There should be 2-3 layers of sponge fingers.)
Smooth over the top of the Tiramisu, using a rubber spatula. Chill in the refrigerator, lightly covered, for 4 to 5 hours.
Just before serving, sift cocoa powder over the Tiramisu, using a fine sieve.