Heat the oven to 175 °C. Line two springform tins (diameter 15 cm) with SAGA Baking Paper. Line the sides of the tins with baking paper as well.
Beat the sugar and eggs until light and fluffy. Combine the flour, potato flour, baking powder and cardamom, and add them to the egg-sugar mixture through a sieve one-third at a time. Mix carefully with a round beater to avoid leaving lumps of flour in the batter. Divide the batter among the tins and bake for about 25 minutes on the lowest rack. Once the cakes have cooled down, cut them into two layers each.
Soak the gelatine sheets in cold water. Crush the lingonberries and combine with the sugar to form a fine purée. Set aside two tablespoons of the purée and combine the rest with the quark. Melt the chocolate and set aside. Whip the cream until fluffy. Heat the lingonberry purée you set aside and dissolve the soft gelatine sheets into it. Mixing continuously, pour the gelatine mixture in a thin ribbon into the lingonberry-quark mixture. Add the chocolate and, finally, fold in the whipped cream.
Line the cake tin with a very high edging of baking paper. Set the first layer of cake in the tin and moisturise it lightly with lingonberry juice. Spread a third of the filling on the layer. Repeat until you have used all the layers. Let the cake set somewhere cold for at least six hours.
For the frosting, bring the water and sugar to boil in a saucepan. Whisk the room-temperature butter until fluffy. Add the cooled-down sugar water and the finely ground cardamom, and whisk until a very light colour and fluffy. Divide the frosting into three parts and colour two parts with shades of blue. Frost the cake in turns with different shades.
Prepare the shavings of white chocolate by melting the chocolate at a low heat. Use a spoon to lift small mounds of chocolate on a sheet of baking paper. Smooth the mounds into the shape of shavings with a wide brush. Let set and decorate the cake with the chocolate shavings.