Line the base of a 20cm springform cake tin with greaseproof paper. Blitz the ginger snaps in a food processor until they are fine crumbs. Melt the butter and add to the crumbs, stirring well until fully coated. Transfer to the cake tin and press down with the back of a spoon until you have an even layer. Chill in the fridge.
Soak the gelatine leaves for 2-3 minutes in cold water until soft. Heat the cream to boiling point, then remove from the heat. Squeeze the excess water from the gelatine, then add to the cream, stirring until they dissolve. Set aside to cool.
Put the cream cheese, mascarpone, icing sugar and vanilla bean paste into a food processor and add the cooled cream. Process until smooth. Transfer the mixture to the tin and smooth until level. Put in the fridge to chill for a minimum of 4 hours, preferably overnight.
Meanwhile, preheat the oven to 200°C/fan 180°C/gas mark 6. Mix together the flour and sugar in a bowl. Add the butter and rub into the flour and sugar until it resembles coarse breadcrumbs. Spread across a lined baking sheet and bake in the oven for 12-15 minutes, or until golden brown. Leave to cool.
Put the sugar in a heavy bottomed saucepan with 50ml water. Heat over a medium heat and bring to the boil, stirring until the sugar has dissolved. Leave to simmer, without stirring, until the sugar reaches a rich golden caramel colour. Add the cream and reduce the heat. Continue to cook for a further 2-3 minutes. Remove from the heat and set aside to cool completely.
Put the butter and sugar in a pan and heat over a low to medium heat until foamy. Add the apples slices and cook for 6-8 minutes or until soft and sticky, but still holding their shape. Set aside until required.
When the cheesecake is set, remove it from tin and base and sit on a cake stand or serving plate. Pour the caramel over so it covers the top and starts to drizzle down the sides. Decorate with the apple slices, then sprinkle over the crumble. Serve.