1. Whisk together soy sauce and sesame oil in a 9-by-13-inch baking dish. Cut a few slits into the fish on both sides using a sharp paring knife. Transfer to dish; turn to coat.

2. Toss ginger with scallions; stuff some into each fish cavity. Spread remaining mixture on top of fish. Let stand, covered, spooning marinade over fish often, for 30 minutes.

3. Bring water to a boil in a large skillet or wok. Arrange red onion on bottom layer of a 12-inch bamboo steamer. Remove fish from marinade with ginger-scallion mixture still on top, and arrange side by side on onion; reserve marinade. Spread sweet potato and Broccolini on separate sides of the top layer.

4. Set stacked steamer in skillet. Steam, covered, until fish is cooked through and vegetables are tender, about 15 minutes.

5. Meanwhile, bring marinade to a boil in a small saucepan. Cook until reduced by half. Strain through a fine sieve. Serve fish and vegetables with reduced sauce.