Preheat oven to 180C (160C fan-forced). Line the base and sides of a square baking tin with baking paper.
Peel apples, cut into quarters and remove core. Chop each quarter into 2cm chunks. Place in a saucepan with remaining apple layer ingredients, cover and bring to a simmer. Remove lid and cook, stirring for 5-7 minutes for the apples to soften a little around the edges. Turn off the heat and set the apples aside to cool.
Meanwhile, prepare the base and crumble mixture. In a large bowl, combine coconut flour, baking powder cinnamon and coconut oil or softened butter. Rub the mixture together with your fingers until well incorporated. Mix water and rice syrup or honey until the honey dissolves and add to the flour mixture. Work the liquid into the pastry until it resembles a slightly formed dough.
Use 2/3 of the mixture for the base, press firmly into the base and corners of the baking tin making sure the base is flat and of uniform thickness around. Please in the fridge for 5 minutes to chill. If using, add the chopped walnuts to the remaining crumble mixture and set aside.
Meanwhile, using an electric mixer or whisk, in a large bowl combine the cheesecake layer ingredients until smooth.
Remove the tin from the fridge, dot the base around with a fork and bake for 10 minutes. Remove from the oven, and pour in the cheesecake mixture flattening the top with a spoon. Bake for 30 minutes. Once the cheesecake layer is set (it will a little seem wobbly), top with the stewed apples and remaining crumble mixture, mixed with the nuts, if using. Bake for a further 10 minutes.
Serve warm or remove from oven and allow to chill on a wire rack for a few hours before refrigerating and serving the cheesecake crumble cold. Be mindful that the cheesecake will be of a fairly soft, creamy consistency, especially when still warm.