For the pear sorbet, put 665ml/23fl oz water in a pan with the sugar and glucose and bring to the boil. Put the pear purée in a mixing bowl. Pour the syrup over the purée and whisk well. Leave the mixture to cool, then pour into a container, cover and freeze for 24 hours. Cut the mixture into rough cubes.
Blend the cubes in a blender until smooth and lighter in colour. Place back in the container, cover and refreeze until set. Alternatively, freeze in an ice cream machine
For the brown-sugar cheesecake, preheat the oven to 190C/170C Fan/Gas 5. Line a 20x30cm/8x12in baking tray with baking paper.
Put the brown sugar in a blender and pulse. Add all the remaining cheesecake ingredients and blend until fully combined. Pour into the lined tray. Bake for 10 minutes. Reduce the oven temperature to 110C/90C Fan/Gas ¼ and bake for a further 25 minutes. It should still have a slight wobble.
Turn off the oven and leave the cheesecake to cool in the oven for 1½ hours. Leave the oven door open for a cheesecake that's creamy in the centre, or leave it closed if you prefer a drier texture.
For the feuilletine base, melt the chocolate in a heatproof bowl set over a pan of gently simmering water, making sure the bowl doesn't touch the water. Leave to cool a little. Blend the pistachios, hazelnuts, flaked almonds, sugar and hazelnut oil in a blender to a course consistency. Transfer to a mixing bowl and mix in the nibbed almonds and feuilletine. Mix in the melted chocolate. Spread the mixture between two pieces of silicon paper to a 5mm/¼in thickness. Store in the fridge for 1 hour, or until fully set.
Remove the top sheet of silicon paper. Trim to the size of the cheesecake tray, reserving the trimmings. Turn out the cheesecake onto the base and return to the fridge.
For the blow torch pear, put equal amounts of sugar and water and bring to a boil. Add the pear and poach for 20 minutes. Remove from the heat and lift the pear out of the sugar syrup. Leave to cool, then cut into 1cm/½in cubes. Sprinkle over the sugar and use a blow torch to caramelise the sugar lightly.
For the tomato caramel, carefully blow torch the tomatoes, then leave to cool. Peel off the skins, then quarter the tomatoes and discard the pulp. Weigh out 400g/14oz tomato flesh and set aside.
Place the sugar in a heavy-based pan and heat until it reaches a walnut brown, to make a dry caramel. Stir in tomato flesh. Simmer for 10 minutes, or until the tomatoes have broken down. Stir in the lime zest and juice. Remove from the heat and leave to cool completely. Transfer to a squeezy bottle and refrigerate.
To assemble, cut the cheesecake into eight 5x11cm/2x4in pieces. Place each in the centre of a plate. Break up the feuilletine trimmings and scatter on the plates, sticking two out of each slice of cheesecake to give height. Scatter around cubes of poached pear. Add a spoonful of pear sorbet. Drizzle the cold tomato caramel around the each plate and serve.