Grind the cardamom pods using a mortar and pestle until they break open. Remove the husks and grind the remaining small seeds to a fine powder.
Put the beets in the mixing bowl of a food processor and blend. Reserve 25 grams of the beets for the icing. While the food processor is running, mix in the egg yolks one by one and then add the oil. Add the sugar and mix until blended. Sieve the flour, cocoa and baking powder over the mixing bowl. Add a dash of salt and ground cardamom and mix to form a smooth batter. Pour in the melted chocolate and continue to mix.
In a clean bowl, whip the egg whites until stiff. First, spoon 1/3 of the egg white mixture into the batter and then fold in the remaining mixture as gently as possible. Pour the batter into a greased cake tin with a diameter of 24 cm.
Bake the cake approximately 45 minutes until cooked through.
For the icing, blend the reserved 25 g of beets, the cream cheese, butter, icing sugar and (ground) cardamom.
Allow this icing to set for at least an hour in the fridge.
Cut the cake horizontally into two equal rounds and spread 1/3 of the icing over the bottom half of the cake. Place the other half on top and cover the entire cake with a layer of pink icing.
Allow the cake to set once more in the fridge before serving.