Make the teriyaki sauce: In a medium saucepan over high heat, add the soy sauce, mirin, water, vinegar, brown sugar, garlic, and ginger. Stir to combine and bring it to a boil. Cook for 3 to 4 minutes. Mix the cornstarch with 1 tablespoon of water to form a slurry and add it to the boiling mixture. Cook and stir until the sauce thickens. Reduce the heat to low and keep warm.
Season the codfish with salt and pepper, to taste. Dust the fillets lightly with flour, shaking off any excess. In a large skillet over medium-high heat, add a thin layer of oil. When the oil is hot, add the codfish and cook until it's browned on both sides and cooked through, about 8 minutes. Remove the fish to a plate and keep warm. Cook the scallions in the same pan, adding more oil if necessary, until they are browned and have softened slightly.
Heat another saucepan over medium-high heat, add a thin layer of oil, and cook the ginger and chile pepper until they are softened, about 2 minutes. Carefully pour in the white wine and cook until it has almost evaporated. Stir in the heavy cream and reduce it by half. Pour in a 1/2 cup of the teriyaki sauce. Add the mussels, cover, and cook until the mussels have opened, about 5 minutes.
Put 2 scallions on each serving plate and arrange a piece of fish on top. Add a few mussels and spoon over some of the cream sauce. Drizzle each plate with extra teriyaki sauce and garnish with chervil leaves.