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Heat oven to 160C/140C fan/gas 2. Line the base of a 22cm round, springform tin with baking parchment. Put the biscuits in a food processor and whizz to fine crumbs. Tip into a bowl, add the melted butter and mix well. Press the biscuits into the base of the cake tin and put in the fridge to chill.
Beat together the cream cheese and sugar with an electric hand whisk until smooth. Carefully add the eggs, 1 at a time with the lemon zest and vanilla extract until well mixed, but don’t overwhisk. Pour the mixture onto the chilled biscuit base and bake in the middle of the oven for 50 mins until just set. Set aside to cool for 10 mins, then remove from the tin and allow to cool completely.
Meanwhile, turn the oven up to 200C/180C fan/gas 6. Put the plums, blackberries and sugar in a large roasting tin and toss together well. Bake in the oven for 10-12 mins until the fruits have collapsed and the sauce is syrupy. Remove from the oven and leave to cool.
When the cheesecake is completely cooled, spoon the soured cream over the top and spread in a thin layer. Serve in wedges topped with some of the baked plums and blackberries, and the rest on the side.