In a bowl, combine the ingredients for the brine with 1 tsp salt. Put the chicken in the brine, cover with cling film and marinate in the fridge for at least 3 hrs.
To make the mayo, combine all the ingredients and stir until smooth.
Half an hour before cooking, remove the chicken from the fridge. Crack the egg into a bowl and whisk with 2 tbsp of the brine. Mix the rice flour and panko, and spread out in a layer on a plate. Remove one chicken breast from the brine, shake off the excess, dip into the egg mix, then coat in the panko mix. Transfer to a plate and repeat with the other chicken breast.
Heat the oil in a deep-fat fryer or large, heavy-bottomed saucepan until it reaches 180C, or a piece of bread browns in 30 secs. Fry for 10-12 mins until cooked through. Drain on kitchen paper, then slice each breast into 4-5 pieces.
Split and toast the buns, then spread with the mayo. Add a layer of lettuce, spring onions and radishes, then top with the chicken and more mayo.