Heat the peanut oil in a sauté pan (preferably nonstick) over medium heat. Add the mushrooms, ham, ginger, and garlic. Cook, stirring occasionally, until the mushrooms are tender, 2 to 3 minutes. Set aside to cool.
Meanwhile, bring a few inches of water to a boil in your steamer. (If you don't have a bamboo steamer, you can use a pot with a flat-bottom steamer insert, or you can rig your own steamer. Just cut the top and bottom from a tuna can to use as a support for the plate and find a covered pot deep and wide enough to accommodate everything.)
Put the fish on a heatproof plate that will fit in your steamer. Sprinkle the mushroom mixture on top. Drizzle with the sherry and sesame oil. Carefully put the plate in the steamer. Cover and steam until the fish is just cooked through, about 10 minutes. See How to tell when fish is truly cooked.
Transfer the fish and juices to serving plates. Drizzle with the soy sauce, sprinkle with the scallions, and serve immediately.