Make the miso sauce. Put the miso paste, soy sauce, sake, mirin and sugar into a small saucepan and heat gently until the sugar has dissolved. Simmer gently for about 5 minutes, stirring frequently. Remove from the heat and set aside to cool.
Arrange the cod fillets in a dish into which they fit snugly and cover with the cold miso sauce. Rub the sauce over the fillets so that they are completely covered and leave to marinate for at least 6 hours, preferably overnight.
Heat a frying pan over a medium heat, remove the cod fillets from the miso sauce and cook the fish for about 2–3 minutes. Carefully turn them over and cook for a further 2–3 minutes. Remove and keep warm.
Heat a clean pan. Brush a little oil over the cut side of the pak choi and arrange them, cut-side down, in the pan. Cook for about 2 minutes until hot and lightly charred. Transfer to a serving plate with the cod and serve immediately.