In a medium bowl, whisk together the white miso paste, sake, mirin, sugar, soy sauce, and sesame oil until smooth.
Place the black cod fillets in a shallow dish or resealable plastic bag and pour the miso marinade over the fish, ensuring it is well coated. Cover or seal and refrigerate for at least 24 hours, up to 48 hours for deeper flavor.
Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
Remove the black cod from the marinade, allowing excess to drip off. Place the fillets on the prepared baking sheet.
Bake in the preheated oven for 12-15 minutes, or until the fish is cooked through and flakes easily with a fork.
Optional: For a caramelized finish, broil the fish for an additional 2-3 minutes at the end of baking.
Serve the black cod over cooked rice and garnish with sliced green onions.