Preheat the oven to 180°C fan-forced. Grease a 23cm springform tin and line with baking paper.
To make the crumble, combine the ingredients in a food processor and process until crumbly. Transfer to a bowl and set aside.
For the cake, place the apples into the food processor and process until finely chopped. Add the remaining ingredients and process for 1 minute. Pour into the prepared tin and sprinkle with the topping.
Bake for 1–1¼ hours, until a skewer inserted into the centre comes out clean. Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Serve with ice cream, caramel sauce, or both.