Preheat the oven to 180C/350F/Gas 4.
For the crumble topping, tip the flour, sugar and cinnamon into a bowl. Rub in the butter with your fingertips until the mixture resembles breadcrumbs. Stir in the milk and set aside.
For the biscuit base, mix the melted butter and crushed biscuits together in a bowl, then press the mixture into the base of 23cm/9in springform tin. Leave to chill in the fridge for 30 minutes.
For the filling, cook the apple slices in a pan of boiling water for 1-2 minutes, or until just tender but still holding their shape. Drain and cool.
Beat the mascarpone and cream cheese in a large bowl until smooth. Beat in the sugar, vanilla seeds and soured cream and beat until smooth. Beat in the eggs, one at a time, until well combined.
Spoon half of the filling onto the chilled biscuit base. Top with the apple slices and sultanas (if using) and sprinkle over the spices, then spoon over the remaining mixture.
Bake for 30 minutes, then open the oven door, pull the cheesecake out a little bit and sprinkle the crumble topping over the top. Shut the door and bake for a further 40-45 minutes, or until the cheesecake is mostly set with a slight wobble in the middle.
Turn off the oven and leave the cheesecake in the oven for two hours, then remove from the oven and set aside to cool completely.