Whisk together the miso, sake, mirin, soy sauce, oil, and sugar. Rub the mixture over every surface of the fish fillets. Transfer to a plastic zipper-lock bag or sealable container. Proceed immediately to the next step, or for best results, marinate for about 30 minutes or up to 2 days.
Adjust a broiler rack to 4 inches from the heat source and preheat the broiler (or toaster oven broiler) to high. Cover a small broiler pan with aluminum foil.
Place the black cod fillets skin side down on the pan. Broil until the top surface is well charred and a thin skewer inserted into the fish shows no resistance at all when piercing through the layers of flesh, about 10 minutes. If any areas of the fish threaten to burn, shield them with small pieces of aluminum foil.
When the fish is cooked, carefully remove the pin bones with a pair of tweezers (there should be no resistance), and serve immediately.