Ingredients
For the apples 
50g butter 
3 tbsp sugar 
1 tsp ground cinnamon 
3 apples (roughly 450g), peeled and cored; 2 cut into small pieces and 1 sliced

For the streusel topping 
80g flour 
50g butter
50g light brown sugar 
1½ tsp ground cinnamon 
50g ground almonds 
50g roughly chopped pecans 

For the cake 
140ml sour cream 

½ tbsp lemon juice
2 eggs 
100g butter 
175g light brown sugar 
1 tsp vanilla extract 
200g plain flour 
1 tsp baking powder 
½ tsp bicarbonate of soda
1 tbsp Demerara or granulated sugar 

Method
Heat oven to 180C. 

Heat 50g butter frying pan over medium heat until the butter has melted. Sprinkle in the sugar and cinnamon and stir. Add the apple slices and mix through the butter. Push the apple slices over to one side leaving some of the caramel and add the pieces of apples into the sauce on the opposite side of the apple slices, you want to keep the two apples separate, this just means you only use one pan and only have to do this process once. Cook until the sauce is sticky (the consistency of golden syrup) - around 5 minutes - and the apples are softening, stirring from time to time, just be mindful not to mix the slices and pieces. Put to one side. 

While the apples cool, make the topping. Rub together the flour and butter until the mixture resembles breadcrumbs. Stir through the brown sugar, cinnamon, almonds and half of the pecans and put to one side. 

To make the cake, mix the eggs, lemon juice and sour cream in a jug.  Place the butter and the sugar in a bowl or mixer and mix until light and fluffy (3-5 minutes). Add the vanilla extract and then the sour cream mixture and mix thoroughly.  The mixture may well look curdled at this point but don't be alarmed, when the flour goes in this goes away. Add the flour, baking powder and bicarbonate of soda and gently stir together until combined, stir through the apple pieces and most of the caramel. 

Grease and line a 20cm cake tin.  Pour in the cake mixture, smooth the top with a spoon and top with the apple slices and any remaining caramel.  Top with streusel topping mixture, scatter with the remaining pecans and the 1 tbsp of sugar and cook in the oven for 1 hour or until a skewer inserted into the cake comes out clean.  

If at any point the cake looks as though it is browning too quickly, cover with foil. 

Variation:
Apple and blackberry streusel - remove the cinnamon in the apples and replace with 1 tsp vanilla.  Remove the cinnamon from the crumble topping.  Add 150g blackberries, mixing half in with the cooked apple pieces, just gently crushing to break up.  Scatter the remaining blackberries over the top of the apple slices before topping with the crumble. 

Peach streusel - replace the cinnamon with vanilla and add ¼ tsp of ground cardamom and replace the apples with fresh or tinned peaches.  In the streusel topping, take out the cinnamon and replace with ¼ tsp of cardamom.  Replace the pecans with pistachios. 

Plum streusel - add 1 star anise to the butter and melt.  Once the butter has melted, put to one side for half an hour.  After half an hour, heat the butter and carry on.  Replace the apples with plums.  In the streusel topping, replace the pecans with hazelnuts. 

Coffee and pecan streusel - Remove the fruit layer completely.  Double the streusel topping mixture.  Take 1/3 out and add 1 tbsp of kahlua or strong cold coffee.  Put half of the cake batter into the tin and then spoon over the 1/3 streusel coffee mix. Add the rest of the cake batter and then scatter over the remaining streusel mix and bake as above. 

Pear and mincemeat streusel - replace the apples with pears and the cinnamon with vanilla.  Spoon the cake mix into the tin and top with 4 tbsps of mincemeat and then the pears.  Replace the pecans with hazelnuts and top with the streusel mix and bake as above.