Combine the mirin and sake in a small saucepan, bring to a boil over high heat. Boil 20 seconds, taking care not to boil off much of the liquid, then turn the heat to low and stir in the miso and the sugar. Whisk over medium heat without letting the mixture boil until the sugar has dissolved. Remove from the heat and whisk in the sesame oil. Allow to cool. Transfer to a baking pan.
Pat the fish fillets dry and spoon on glaze, covering both sides. Place fish in baking dish and turn them over a few times in the marinade remaining in the dish. Cover with plastic wrap and marinate for 2 to 3 hours, or for up to a day. Keep excess glaze to use for plating.
Light the broiler. Line a sheet pan with foil and lightly oil the foil. Tap each fillet against the sides of the bowl or dish so excess marinade will slide off. Place skin side up on the baking sheet if broiling.
Place the fish skin side up under the broiler, about 6 inches from the heat. Broil for 2 to 3 minutes on each side, until the surface browns and blackens in spots. Slightly longer per side if it is a particularly thick piece of fish. If you have any sauce left, spoon it over the hot fish.
