Season the fish pieces with salt, two tablespoons of the chopped coriander, half the chilli, the lime zest and smoked paprika in a bowl. Set aside for at least 30 minutes and preferably a few hours.
Put the wine, vinegar, sugar and 100ml/3½fl oz of water in a pan and heat to a simmer.
Place the carrots, shallot, garlic and green chilli into a bowl and pour the simmering pickling juice over. Submerge the carrots using a piece of cling film to hold them in place. Leave to cool.
To make the batter, mix together the flour and cornflour with a pinch of salt in a bowl. Add the soda water and keep the batter chilled, ideally on ice, until needed.
Preheat a deep fat fryer to 180C/350F, or half-fill a heavy-bottomed pan with sunflower oil. (Caution: hot oil can be dangerous. Do not leave unattended.) Dust the fish with flour and pat off any excess.
Dip the pieces of fish into the batter and carefully drop them into the fryer one by one. Cook for two minutes and then transfer to a on a plate lined with kitchen paper. Season the crispy batter with a touch more salt.
Drain the carrots and discard the garlic. Mix the remaining tablespoon of chopped coriander and the spring onions with the carrot mixture, season with salt and dress with the rapeseed oil. Serve the fried fish on a platter with the pickled carrot salad.