For the miso halibut, mix the miso paste, sugar, soy sauce, sake and mirin together in a large glass bowl until well combined.
Add the halibut fillets and mix until completely coated in the marinade. Cover the bowl and chill in the fridge and marinade for at least four hours, or preferably overnight.
Meanwhile, for the prawn dumplings, blend the chopped prawns, soy sauce, mirin and ginger in a food processor for 12-15 seconds, or until roughly combined. Transfer the mixture to a bowl and stir in the spring onion.
Place three wonton wrappers onto a chopping board and place one teaspoonful of the prawn mixture into the centre of each.
Brush the edges of the wonton wrappers with a little of the beaten egg mixture, then fold each wrapper in half over the mixture, to form a triangle shape, and seal the edges together.
Repeat the process with the remaining wonton wrappers and filling mixture.
Wrap a filled wonton wrapper around your finger so that the two corners at the base of the triangle meet. Press these two corners together (the dumpling should resemble a tortellini.)
Repeat the process with the remaining filled wontons.
Chill the prawn dumplings in the fridge until needed.
When the halibut fillets have marinated, preheat the grill to its highest setting.
Remove the halibut fillets from the marinade, shaking off any excess, then transfer them to a lightly oiled baking tray. Grill for 5-6 minutes, turning once during cooking, until just cooked through. (NB: The halibut is cooked through when the flesh is opaque.)
Just before serving, bring a pan of salted water to the boil. Add the prawn dumplings to the boiling water, in batches, and boil for 2-3 minutes. Remove from the pan using a slotted spoon and set aside to drain on kitchen paper. Repeat the process with the remaining dumplings.
Meanwhile, for the shiso broth, bring the stock, sake, soy sauce, ginger, sugar and salt to a simmer in a saucepan.
Add the vegetables and simmer for 2-3 minutes, or until just tender, then add the dumplings to the broth and heat until warmed through.
To serve, place three prawn dumplings into each of four warmed serving bowls. Pour over the broth and vegetables. Add two shiso leaves to each bowl, then top each portion with a grilled halibut fillet. Sprinkle each dish with a pinch of shichimi pepper.