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Sift the flours into the bowl of a food processor then add the sugar, baking powder and salt. Add the butter and eggs and process them until they form a batter. (You can also do this in a large bowl with a handheld electric mixer.)
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Tip the batter into a large bowl and gently fold through the grated courgettes and the caraway seeds.
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Divide the mixture equally between the two lined cake tins and cook for 25–30 minutes or until golden-brown and springy to the touch. Remove from the tins and cool on a rack.
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For the filling, grate the apples into a pan and add the apple juice as required to keep apples moist. Add the sugar and bring the mixture to a simmer, stirring occasionally until the apples are softened, caramelised and all obvious wateriness has gone. Turn off the heat and leave to cool.
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Add the butter and the cooled apple mixture to the bowl of a large food processor and blend to a purée. Stir this into the softened cream cheese and set aside.
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For the topping, toast the oats in a dry frying pan until golden-brown and aromatic, then add the sugar to caramelise the oats.
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Once the cakes are cool, spread a thick layer of the filling on onto one cake. Gently place the other cake onto the top, then spread a thinner layer of icing on top. Sprinkle with the toasted oats and serve.
