Line the base of a 20 cm springform pan with baking paper. Mix the biscuit crumbs with melted butter, press firmly over the base, and chill while preparing the filling.
Beat the softened cream cheese, icing sugar, and vanilla until smooth and free of lumps.
Fold the cooled melted chocolate into the cream-cheese mixture until evenly coloured.
Whip the cold cream to soft peaks, then gently fold it through the chocolate mixture without deflating it.
Spoon the filling over the chilled crust and smooth the top. Cover and refrigerate for at least 6 hours, preferably overnight, until firm.
Release the cheesecake from the pan, add the optional chopped chocolate topping, and slice with a warm, dry knife.