Line the edge of an appropriately sized cake ring with a cake collar. Dip half of the sponge fingers in the mixture of simple syrup and rum and use them to cover the floor of the mould. Soak the gelatine in cold water.
In a mixing bowl placed over a bain-marie heated no warmer than 65 °C (to prevent the eggs from solidifying), beat the eggs and the sugar. Then use a food processor to beat this mixture until it has cooled down to just above body temperature. Whip the cream until half-stiff. Dissolve the soaked gelatine in a bit of cream over the bain-marie, thereafter folding it into the egg-and-sugar mixture. Continue by folding in the whipped cream in three steps.
Distribute part of the resulting cream mixture on the sponge finger base. Then lay down a further layer of soaked sponge fingers, followed by another layer of cream. If you still have some cream left, you can save it to pipe rosettes onto the cake with a star nozzle later on.
Chill the cake in the refrigerator for 3–4 hours. Before serving, remove the cake ring and the collar and complete by decorating the cake’s edge with the shaved almonds.