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Butter and line the base of a 23cm loose-bottomed cake tin. Whizz the biscuits to a rough crumb in a food processor, or put them in a sandwich bag and crush with a rolling pin. Tip the crumbs into a bowl with the melted butter, stem ginger and spices, and stir well. Press the mixture into the tin, pushing up the sides a little (putting your hand in a food bag makes this easier). Leave the base to set for 30 mins in the fridge.
For the cheese layer, whisk all the ingredients together until smooth, then pour over the base. Chill in the fridge overnight.
The next day, make the topping. Mix the cinnamon, ginger and mixed spice in a large bowl. Cut each apple into 12 wedges, then toss the wedges in the spice mixture. Heat the sugar and 4 tbsp water in a saucepan and bubble to a caramel. As soon as the sugar becomes a dark caramel, take off the heat and carefully toss through the apples. Pour in the brandy, and the whole lot will bubble and seize. Return the pan to the heat and simmer gently to re-dissolve the caramel and cook the apples in the syrup. Remove from the heat and set the apples aside to cool in the syrup.
Ease the cheesecake out of the tin. Spoon the apples over the top with a slotted spoon. Serve the sticky brandy syrup on the side as a sauce.