To make this speedy sheet pan recipe a success, nestle salmon fillets into the pan once the vegetables have softened. A blast of high heat crisps the skin but doesn't overcook the fish.
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 of 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.