Soak the dried shiitake mushrooms in a bowl with 2 cups of hot water for 2 hours, or until reconstituted. Squeeze the water from the mushrooms, trim off any tough stems, and cut the mushrooms in half. Reserve 1 cup of the soaking liquid, avoiding any sediment that may have settled at the bottom of the bowl, and set aside.
Rinse the fish pieces and pat dry with a paper towel. Place the fish in a bowl along with the cornstarch, flour, Shaoxing wine, salt, and sesame oil. Mix well to coat the fish, and marinate for at least 30 minutes or overnight.
Next, make the sauce mixture. Combine the reserved cup of mushroom soaking liquid with 1 tablespoon Shaoxing wine, the oyster sauce, chee hou sauce, light soy sauce, sesame oil, and white pepper. Mix well and set aside.
Place your wok over high heat until it just starts to smoke, and add the oil, making sure to coat the sides of the wok. Stir the fish in the marinade ingredients to make sure it’s uniformly coated. Quickly and carefully, place each piece of fish into the oiled wok in a single layer.
Reduce the heat to medium-high, and let the fish fry undisturbed for 1 minute. Then carefully flip the fish pieces and fry for another minute. Turn off the heat, and transfer the fish pieces to a plate. Set aside.
With the wok over medium heat, add the ginger slices. Cook for 15 seconds, and then stir in the white parts of the scallions. Cook for another 30 seconds, and then add the garlic, carrots, and shiitake mushrooms. Stir-fry for 30 seconds.
Next, add the prepared sauce mixture and the firm tofu. Gently stir everything together, and bring the mixture to a simmer. Simmer for 2 minutes.
Add the fish back to the wok, and simmer for another 2-3 minutes, until the fish is heated through. While the fish is simmering, place a clay pot on the stove over medium heat for 1-2 minutes. Add the lettuce to the clay pot.
To finish the dish, drizzle in the cornstarch slurry while gently stirring everything together. The sauce should thicken nicely. Add the green portions of the scallions and cook for a few seconds, just until they start to wilt. Scoop the fish mixture into the clay pot over the iceberg lettuce. It should be bubbling! Serve immediately.