For the cake layers: Preheat the oven to 350 degrees and set rack at middle level. Butter a 9 or 10-inch round cake pan and line the bottom with a disk of parchment or waxed paper. Whisk yolks with half the sugar and vanilla until thick and light. In a clean, dry bowl, whisk whites with salt and continue whisking until they are white and opaque. Whip in remaining sugar in a stream. Continue whipping whites until they hold a firm peak. Fold yolks into whites then sift over and fold in flour and starch. Scrape batter into prepared pan and smooth top. Bake about 30 minutes, until well risen and deep in golden color. Unmold to a rack to cool.
For the custard cream: Bring milk to a boil with half the sugar in a heavy, non-reactive pan. Whisk yolks with remaining sugar and sift over and whisk in flour. When milk boils, whisk a third into the yolk mixture. Return the remaining milk to a boil and whisk in yolk mixture, continuing to whisk until the mixture thickens and comes to a boil. Whisk constantly 30 seconds. Remove from heat and whisk in vanilla. Scrape half the cream to a bowl and cover with plastic wrap, refrigerate to cool. Whisk chocolate into remaining cream and scrape into a bowl, cover and cool.
For syrup: In a small saucepan, bring water and sugar to a boil. Cool and stir in rum.
For whipped cream: Combine all ingredients and whip to a soft peak.
To assemble: Cut cake into thin, vertical slices. Place a layer of slices in the bottom of a glass serving bowl and moisten with syrup. Spread with half the vanilla cream and scatter with half the raspberries. Continue alternating layers to make 2 layers each, vanilla/raspberry, chocolate and whipped creams, ending with whipped cream. Sprinkle lightly with chocolate shavings and a few raspberries.