Drain tofu and gently invert onto a thick layer of towels on a flat surface. Pat dry and let drain about 5 minutes.
Meanwhile, make marinade: In a medium bowl, combine black-bean garlic sauce, Shaoxing rice wine, sesame oil, soy sauce, dark soy sauce, garlic, and sugar. Set aside.
Pour 1 to 3 in. water into bottom of a steamer (see "Steaming Setups," below). Place rack at least 1 in. above surface of water. Cover and bring to a boil over high heat.
While water is coming to a boil, cut tofu in half lengthwise, then cut each half crosswise into rectangles about 1/2 in. thick. Lay tofu in a single layer in a 9- to 10-in. heat-resistant glass pie pan; save any pieces that don't fit for another use.
Rinse fish, pat dry, and cut into pieces about the same size as tofu. Add fish to reserved marinade and mix to coat. Lay fish on tofu and spoon marinade on top. Sprinkle ginger evenly over fish.
Set pie pan on rack. Cover and steam until fish in center is barely opaque in thickest part (cut to test), 6 to 8 minutes (fish will continue to cook after you remove it from heat).
Turn off heat. Carefully lift pie pan from steamer. If it's difficult to remove, slip a wide spatula under pie pan to lift up, then grasp pie pan with a pot holder (or use two sets of tongs). Sprinkle with green onions.
Steaming Setups. All you need is a vessel to hold water, a rack to suspend the food over the water, and a lid to keep the steam in. Here are some possible combinations.
Wok and rack: A 14- to 16-in. wok with a domed lid and steamer rack or a round cake rack. Set wok on a ring if it wobbles. Put rack right in wok; the sloped sides will hold the rack over the water. The wide opening makes it relatively easy to remove the cooked dish. Woks run from $15 to $150 or more, and are widely available.
Bamboo steamer: Chinese stackable bamboo steamer baskets with lids. Set a 10- to 12-in. basket right in a 14- to 16-in. wok (make sure the bottom rim is just covered by water, as the baskets scorch easily; add boiling water as needed). Layer baskets to cook more than one dish. Bamboo steamers are generally $15 to $20 and are widely available.
Metal steamer: Chinese steamer pan topped with stackable baskets and a domed lid. Choose a 10- to 12-in.-wide steamer for greatest versatility. Stackable baskets can cook several dishes at a time. Metal steamers cost from $30 to $35 and may be found at Asian markets.
Western-style: A deep, wide pan or kettle with a lid, a round cake rack, and 3 empty cans. Set 2- to 3-in.-tall cans (both ends removed) into pan (or use the removable rim of a cheesecake pan). Top with a round cake rack and place pie pan on it; cover to steam.
Note: Nutrition analysis is per serving.