Preheat the oven to 425°F (220°C) with a rack in the center position.
Thinly slice the mushrooms and spread them out in a large 9 x 13 inch (23 x 33 cm) baking dish. Add 4 tablespoons of the minced ginger, the minced garlic, toasted sesame oil, and soy sauce to the dish and gently toss everything together. Season with salt and pepper.
Roast for 15 minutes, tossing once or twice, until the mushrooms are soft and the juices have released. Remove from the oven and season with salt and pepper to taste.
Slice the fish into 4 ounce pieces and season generously with salt and pepper. Rub the tops of the fish with the remaining minced ginger. Place the fish on top of the cooked mushrooms, spacing them apart by an inch or so, and bake for another 8 to 12 minutes, or until the fish is just cooked and flakes easily with a fork.
Serve immediately with steamed rice and sautéed baby bok choy or another leafy green.