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Brush a 20 x 30cm baking tin with a little oil, then line well with two layers of cling film, leaving overhang for lifting out – or use a tin with a loose bottom. Put the biscuits into a food processor and whizz to crumbs, then tip in the melted butter and mix again. Press the crumbs firmly into the base of the prepared tin, then chill while you make the filling.
Put the cream and chocolate in a small pan. Melt very gently, stirring, until no lumps of chocolate remain. Clean out the food processor and add the raspberries and creamy chocolate mixture. Whizz together until it can’t get any smoother, then rub through a sieve to get rid of the raspberry seeds.
Put the cream cheese into a mixing bowl with the sugar and the sieved raspberry mixture. Beat with an electric whisk until smooth.
Let the ice cream soften in a big bowl, but not melt, then fold in the cream cheese mixture a little at a time until well mixed and no ice-cream lumps are visible. Scrape into the prepared tin and level the top. Cover with cling film, not letting it touch the top of the cheesecake, then freeze at least overnight or up to 3 months before serving.
To serve, remove the covering cling film, lift out the cheesecake, or slide out if in a loose-bottomed tin. Remove any remaining cling film. Decorate the top with fresh raspberries and drizzle with a little more melted white chocolate.