Whisk 1/4 cup sake, ponzu, hoisin, and 2 tablespoons soy sauce in a small bowl.
Place fish in a gallon-size resealable plastic food storage bag and pour sake mixture over fish. Turn to make sure fillets are well coated and push out as much air as possible before sealing. Marinate for 30 minutes to 1 hour, turning over bag halfway through. Remove fish from marinade and dry with paper towels. Season fish on both sides with salt and white pepper. Put rice flour in a small container and lightly dredge fish, shaking to remove any excess flour.
Heat 2 tablespoons vegetable oil in a large saute pan over medium-low heat. When hot, add fillets and saute until lightly browned on both sides and cooked through, 4 to 6 minutes total. Transfer to a paper towel-lined plate and set aside until ready to serve.
In a medium saucepan, add dashi broth, remaining 1/2 cup sake, remaining 1 tablespoon oil, and green onions and cook until slightly reduced and sauce looks a bit concentrated but is still brothy, about 5 minutes. Remove from heat and whisk in miso and 1/4 teaspoon soy sauce. Place fish in centers of bowls. Stir in edamame and enoki mushrooms and spoon broth into shallow serving bowls.
Place pea sprouts in a small bowl with sesame oil, remaining 1/4 teaspoon soy sauce, sea salt, and black pepper, and toss to coat. Place a small amount of sprouts on top of fish to garnish; serve immediately.