Preheat oven to 350 degrees F. Separate eggs into two bowls. Divide sugar and add half to each bowl. Beat both mixtures very well, the whites until peaks form. Fold egg whites into yolk mixture. Gradually add flour, mixing with a wooden spatula. Mix in the butter. Pour batter into 10-inch round greased cake pan. Bake about 20 minutes, or until spongy and golden. Remove from oven and allow to cool fully.
Custard Pastry Cream
In a saucepan, heat butter, milk, and light cream to just below a boil. While this mixture is cooking, combine sugar, cornstarch, and eggs in a bowl. Whip until ribbons form. When the butter-cream mixture reaches the boiling point, slowly whisk in the sugar-egg mixture and cook to boiling, stirring constantly. Boil for 1 minute. Pour into a bowl and cover the surface with plastic wrap (to prevent crusting). Chill overnight if possible. When thoroughly chilled, whisk to smooth out and flavor with dark rum.
Chocolate Icing: Melt semisweet chocolate in a small saucepan. Thin with warm water to desired consistency.
White Icing: Heat corn syrup with water. Add confectioners’ sugar and warm to 105 degrees F.
Assembly: Level Sponge Cake off at the top with a slicing knife and cut in half to make two layers. Spread Custard Pastry Cream over one layer, reserving a small amount of custard to spread on the sides to help almonds adhere. Top with second cake layer. Spread a thin layer of Chocolate Icing on top of cake. Using White Icing in a pastry bag (with a ⅛-inch tip), follow immediately with spiral lines starting from the center of the cake. Score white lines with the point of a paring knife, starting at the center and pulling outward to the edge. Spread sides of cake with a thin coat of the remaining Custard Pastry Cream, and press on toasted almonds.