Begin by making the cheesecake base. Crush the biscuits to a fine crumb by using a food processor or putting them in a ziplock bag and bashing them up with a rolling pin.
Add the crushed biscuits to a bowl and stir in the melted butter until all the crumbs are coated.
Press the biscuit crumbs into the cake pan. Use the back of a spoon to press them in and get a compacted even layer. You want to press hard - but not too hard or the cheesecake will be very difficult to turn out and cut. Refrigerate until needed.
For the filling, melt the white chocolate in a heatproof bowl over a pan of simmering water. Set aside to cool.
In a large mixing bowl, whisk the mascarpone and creme fraiche until smooth and combined. Fold in the melted white chocolate (make sure it's cool to the touch or it will crystalise) next, add the peppermint extract and vanilla extract and fold until combined.
Spoon the mixture into the cake pan smoothing out the top with a spatula. Refrigerate so it can set while you make the chocolate mousse.
For the white chocolate and peppermint mousse, melt the white chocolate in a heatproof bowl over a pan of simmering water. Set aside to cool.
In a large mixing bowl, beat the double cream, icing sugar and vanilla extract until light and fluffy. Add the cream cheese to the bowl and beat until really smooth and silky.
Fold in the (cooled) white chocolate and crushed peppermint candy canes and gently mix until just combined. The mixture will look creamy and loose, but don't worry it will set! Pour the mousse on top of the cheesecake and put it in the freezer for two hours.
Meanwhile, make the peppermint bark. Melt the white chocolate in a heatproof bowl over a pan of simmering water. There's no need to wait for it to cool, go ahead and spread it on the tray with baking paper. Sprinkle the crushed candy canes over the top and put the tray in the fridge to set.
Once the cheesecake has been in the freezer for two hours, turn it out from the cake pan and decorate the top with the peppermint bark, breaking it into shards and covering the top of the cheesecake.
Leave the peppermint bark cheesecake to stand for 30 minutes and then serve. If you're making ahead you can refreeze the cheesecake, but remember to take it out to defrost 30 mins before serving.