Preheat the oven to 110C/90C Fan/Gas ¼ and line a baking tray with baking paper. Place the cherry tomatoes on the baking tray and roast for 1 hour or until dried out.
For the Thai green emulsion, bring a small saucepan of water to the boil and blanch to coriander and the mint leaves for 2 minutes. Immediately refresh under cold, running water. Drain the leaves and pat dry with kitchen paper.
Place lime leaves, lemon zest, lemongrass, grated ginger, chilli, galangal and 100ml/3½fl oz sunflower oil into a saucepan and gently heat through.
Transfer this mixture into a liquidiser and add the coriander and mint. Blend thoroughly until smooth. Sieve the mixture into a bowl, set aside and leave to cool.
In a food processor, blend the egg, lemon juice, vinegar, mustard and seasoning on a high speed, slowly adding the remaining 300ml/10fl oz sunflower oil until the mixture has thickened. Fold in the cooled, spicy green liquid and set aside.
For the halibut, fill a deep-fat fryer or a large, deep, heavy-bottomed pan two-thirds full with the oil. Heat to 180C (a cube of bread should turn brown in one minute when dropped in.) CAUTION: Hot oil can be dangerous. Do not leave unattended.
In a large bowl, mix the flour and squid ink together, season generously with salt and pepper, then with an electric whisk, incorporate the cold, sparkling water to form a runny batter.
Dip each halibut piece into the batter and shake off the excess. Repeat this process twice for each piece.
Carefully, lower the coated haddock pieces into the deep-fat fryer and cook for 4 minutes or until the batter is crispy and the fish is cooked through. Remove from fryer and drain on kitchen paper.
Dot the emulsion onto the plate and place the fish on top, scatter the cherry tomatoes around the plate.