Preheat the oven and grill to 180C/350F/Gas 4.
For the chilli yuzu paste, blend all of the chilli yuzu paste ingredients except the mirin and vegetable oil in a food processor to a paste.
Gradually add the mirin (or water) and vegetable oil and blend again until all of the liquid has been fully incorporated into the mixture. Set aside.
For the white miso aioli, blend the cooked potato, white miso, garlic and poached egg in a food processor until smooth and well combined.
With the motor still running, gradually add the vegetable oil in a thin stream until it is completely incorporated in the mixture.
Add the ginger juice and lemon juice and blend again until well combined.
For the prawns, lay each prawn on its back. Cut the tail meat and shells in half lengthways using a sharp knife or scissors. Remove the tail meat from the shells and chop roughly.
Stir the chopped tail meat into the chilli yuzu paste.
Return the prawn and chilli yuzu mixture to the shells (there should be two filled shells per person). Place the four prawn halves onto a baking tray and cook for 1-2 minutes.
Remove the prawn halves from the oven. Carefully stir the prawn and chilli yuzu mixture around, in the shells. Return the prawns to the oven and cook for a further 1-2 minutes, or until the flesh is pink and cooked through.
To serve, squeeze the julienned daikon into two cone shapes. Place one cone of daikon onto the end of each of two rectangular serving plates. Sprinkle over the black sesame seeds. Place two filled prawn halves into the centre of each plate. Place the lemon balm leaves on top. Divide the aioli between two dipping bowls. Place them at the other end of the plates.