Grease a 10-inch (25-cm) springform cake pan.
Preheat oven to 375°F (190°C).
To make cake), put egg yolks and a third of the sugar into a large bowl.
Beat until pale and creamy, 5 to 10 minutes with an electric mixer.
Beat egg whites until stiff.
Gradually fold in remaining sugar.
Sift flour with baking powder.
Mix in ground almonds.
Fold egg white mixture into egg yolk mixture.
Fold in flour mixture.
Melt butter; cool slightly.
Stir butter into batter.
Turn into greased pan.
Bake 35 to 40 minutes or until a wooden pick inserted in center comes out clean.
Cool on a rack 2 hours.
To make filling, combine almonds, rum, powdered sugar and water in a medium bowl to make a smooth paste.
Cut cooled cake horizontally into 2 layers.
Join cake layers with almond filling.
Preheat oven to 450°F (230°C).
To make topping, wash and stem gooseberries.
Combine 1/4 cup (50 g) sugar and water in a medium saucepan.
Bring to a boil and add gooseberries.
Simmer over low heat about 10 minutes until gooseberries are soft but not disintegrating.
Drain thoroughly.
Beat egg whites until stiff; beat in remaining sugar.
Fold in vanilla.
Arrange drained gooseberries over cake, reserving 14 whole gooseberries for decoration.
Spread about two-thirds of the meringue mixture thickly over top and sides of cake.
Place remaining meringue mixture in a pastry bag fitted with a fluted nozzle.
Pipe 14 meringue garlands on top of cake, working from center outwards and ending each in a rosette.
Bake 1 minute or until meringue is light golden brown on top.
Decorate center and sides of gateau with almonds.
Top each meringue rosette with a reserved gooseberry.