For the Philadelphia cake, beat the eggs with the sugar until foamy, then stir in the oil and water. Sift flour and baking powder and fold in together with hazelnuts and cocoa.
Spread the batter into a rectangular baking pan and bake at 180° for about 30 minutes. Stir Philadelphia and crème fraîche together until smooth and add vanilla sugar, rum and powdered sugar.
Whip the cream with the cream stiffener and mix with the Philadelphia cream, spread the cream on the cooled slices and finally sprinkle the Philadelphia slice with coconut or chocolate flakes.