Preheat the oven to 160°C/gas mark 3.
For the Parmesan biscuit, mix together the flour, Parmesan and salt and rub in the butter to create a coarse crumble.
Pour the crumble across a baking tray and cook for 10–15 minutes until golden, then remove from the oven and set aside to cool
Meanwhile, lightly score a cross through the skin of each tomato and place in a bowl.
Cover with just enough boiling water to cover and leave for 30 seconds, then drain and cool the tomatoes under cold water. Peel off and discard the skins.
Place 8 of the tomatoes in a heavy-bottomed pan with the butter and thyme sprigs.
Gently melt the butter over a low heat and allow the tomatoes to confit slowly for 1 hour
Place the remaining 8 tomatoes in a vacuum bag with the vinegar and sugar and seal with a chamber sealer to compress. Set aside until ready to serve
Once the pastry crumble has cooled, transfer to a food processor and blend until the fat begins to separate out, making the crumbs sticky and glossy. Tip out onto a tray lined with baking paper and cover with a second sheet.
Roll out evenly to create a thin layer of dough and transfer the tray to the freezer for 1 hour to set
To make the avocado emulsion, remove the peel and stone and place the flesh in a blender with the egg yolks and lemon juice.
Blend briefly to combine as a smooth mixture then, keeping the machine slowly running, gradually pour in the sunflower oil until the mixture emulsifies
Adjust the seasoning to taste, then pass through a fine sieve to ensure the emulsion is completely smooth. Transfer to a piping bag and reserve in the fridge until ready to serve
Drain the confit tomatoes from the butter and the compressed tomatoes from the vacuum bag. Remove the Parmesan dough sheet from the freezer and use a 6cm pastry cutter to stamp out biscuit discs
To assemble the tarts, place a Parmesan biscuit on each plate and stand 2 compressed tomatoes and 2 confit tomatoes on top.
Pipe over a little of the avocado emulsion and some shredded fresh basil.
Gently warm the chorizo slices in a frying pan over a medium heat and lie across the top of the tarts, garnishing the plates with a few salad leaves to serve.