Pre-heat the oven to 190°C and line two 20cm cake tins with parchment.
Toast the caraway seeds in a frying pan over medium heat for 3 minutes.
Process flours, sugar, baking powder, salt, butter, and eggs into a batter.
Fold the grated courgettes and toasted caraway seeds into the batter.
Bake the mixture in the tins for 30 minutes until golden.
Simmer grated apples, juice, and sugar until softened and caramelized.
Purée the apple mixture with butter and stir into the cream cheese.
Toast oats in a pan and add sugar to caramelize.
Sandwich cakes with filling, ice the top, and sprinkle with oats.