Pat the fillets thoroughly dry with paper towels. Slather the fish with Nobu-style miso and place in a non-reactive dish or bowl and cover tightly with plastic wrap. Leave to steep in the refrigerator for 2 to 3 days.
Preheat the oven to 400 degrees F. Preheat a grill or broiler. Lightly wipe off any excess miso clinging to the fillets but don't rinse it off. Place the fish on the grill, or in a broiler pan, and grill or broil until the surface of the fish turns brown. Then bake for 10 to 15 minutes.
Arrange the black cod fillets on individual plates and garnish with hajikami. Add a few extra drops of Nobu-style miso to each plate.
In a medium saucepan combine the sake and mirin and carefully flambe. When the flames die out, add the water and 1/2 cup sugar. Stir until the sugar dissolves. Stir in the miso and, using an immersion blender, dissolve the miso into the liquid. Transfer the mixture to a double boiler and cook until caramel in color and all of the lumps are gone, abut 45 minutes. Cool.
Turn the heat down to low and add the miso paste, mixing with a wooden spoon. When the miso has dissolved completely, turn the heat up to high again and add 1 tablespoon of sugar, stirring constantly with the wooden spoon to ensure that the bottom of the pan doesn't burn. Remove from heat once the sugar is fully dissolved. Cool to room temperature.
Recipe courtesy Nobuyuki Matsuhisa, "Nobu: The Cookbook" Kodansha International, October 2001