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Heat oven to 160C/140C fan/gas 3. Butter a 22cm round loose-bottomed cake tin and line the base with baking parchment. Beat the butter and caster sugar together in a large bowl until it is light and fluffy. Gradually pour in and beat the eggs, a little at a time, until you have used two-thirds, adding flour if it curdles. Fold in the remaining egg, the ground almonds and finally the flour, and combine everything gently.
Add two-thirds of the apples to the cake mixture and all the blackberries. Turn the mixture into the prepared tin and smooth it out evenly. Scatter the remaining apples over the surface of the cake. For the topping, sprinkle over the cinnamon, demerara sugar and butter. Bake for 50-55 mins or until a skewer comes out clean. Remove the cake from the oven and scatter on the toasted hazelnuts. When the cake is cool, dust lightly with icing sugar. Serve in slices.