Rinse fish fillets and pat dry with paper towels. Combine miso, brown sugar, sesame oil and mirin and stir well until brown sugar is fully dissolved.
Brush about 2 tablespoons miso glaze on each fish fillet. Marinate for at least 30 minutes, or up to 1 hour. Place fish under broiler for 3 to 4 minutes, or until top is slightly charred and glaze has caramelized. Remove fish from oven and brush with remaining glaze. Lower oven to 375 degrees F. Cook an additional 5 to 6 minutes, until fish is flaky but not overcooked.
If desired, serve with toasted sesame seeds and scallions.