Preheat the oven to 190 C / Gas mark 5. Brush a 20cm (8-inch) springform tin with oil.
Melt the butter in a pan and add the crushed biscuits, stirring until coated in all the butter.
Spread over the bottom of the tin, pressing down with your knuckles to check it is firmly covering the surface.
Beat the cream cheese, mascarpone, eggs, sugar and vanilla essence in a large bowl until smooth.
Setting aside a bit of cream, whisk the remaining until soft peaks form, and fold into the cream cheese mixture.
Pour over the biscuit base and smooth the top; place on a baking tray.
Melt the chocolate with the remaining cream in the microwave, stirring every 30 seconds. Then dip half the raspberries and place them around the tin.
Crush the leftover raspberries through a sieve and stir in the icing sugar. Spooning the raspberry mixture on top of the cheesecake in a pattern. Using a skewer or small palette knife, gently swirl through the raspberry patches to make a marbled effect.
Bake in the preheated oven until the cake is a bit wobbly in the centre but not liquid, 20 to 30 minutes.
Leave to stand for 20 minutes then chill in the fridge for at least 6 to 8 hours or overnight.