Preheat the oven to 180C/350F degrees.
Line the bottom of a spring-form cake tin with greaseproof or parchment paper.
Melt the butter in a saucepan.
Add the hazelnut flour and sugar substitute. Mix thoroughly until the mixture looks like glossy breadcrumbs.
Spoon the mixture into the cake tin and use a spoon to spread evenly, pressing the mixture down evenly.
Bake in the oven for 15 minutes.
Remove from the oven and place in the fridge to cool.
Place the cream cheese in a bowl and blend with the sugar substitute. I used a hand blender.
Add the eggs, cream, lime juice, lime rind and continue to blend until smooth.
In a separate bowl or even a jug, use a hand blender to blitz the blackberries until smooth.
Add the blackberry mixture to the cream cheese mixture and stir thoroughly until even in colour.
Pour over the hazelnut base and bake in the oven for 30-40 minutes until the centre has a slight firmness. (Don't worry about too much wobble).
Allow to cool, then place in the fridge overnight.