Preheat broiler on high with a rack 8 inches below element. Season fish in a dish with salt and pepper.
Whisk together soy sauce, brown sugar, and vinegar.
Spoon half soy mixture over fish. Let stand 10 minutes, turning a few times.
Meanwhile, on a rimmed baking sheet, toss peppers, asparagus, mushrooms, and scallions with remaining soy mixture and oil; season.
Spread vegetables into a single layer and broil until tender and golden brown in places, 8 to 10 minutes.
Nestle in fish, skin-sides up, and continue broiling until skins are crisp and fish is just cooked through, about 5 minutes.
Chop scallions and stir half into cooked rice; season with vinegar. Serve fish over rice with vegetables, any accumulated juices, remaining scallions, and sesame seeds.
