Beat eggs in medium bowl with electric mixer until thick and creamy. Gradually add sugar; beat until sugar dissolves. Gently fold in flour, cornflour and baking powder. Pour mixture into greased deep 28cm round cake pan. Bake, uncovered, in moderate oven about 35 minutes or until cake is cooked when tested; turn onto wire rack to cool. Wash and dry cake pan.
Split cake, horizontally, into three even layers. Place first layer of cake in clean deep 28cm-round cake pan. Brush cake with combined milk and rum. Spread half of the custard filling evenly over cake. Reserve eight strawberries for decorating top of cake; hull and slice remaining strawberries. Sprinkle half of the sliced strawberries over custard layer. Place second layer of cake on top of strawberries; brush with rum mixture. Spread remaining custard filling evenly over cake; sprinkle with remaining strawberries. Top with third layer of cake; brush with remaining rum mixture. Refrigerate, covered, several hours. [Can be made 2 days ahead to this stage.]
Turn cake onto serving plate. Decorate top of cake with reserved strawberries, blueberries and raspberries; dust top with sifted icing sugar.
To make the custard filling. Combine cornflour, custard powder and sugar in large saucepan. Gradually add milk; stir until smooth. Add essence and cream; stir until combined. Stir over low heat until custard boils and thickens; add butter. Simmer, uncovered, 3 minutes, stirring constantly; remove pan from heat. Add yolks; mix well. Transfer custard to medium heatproof bowl; cover surface with plastic wrap. Allow to become cold; beat well.