In a small saucepan over medium-high heat, combine the sake, mirin, miso paste, and sugar. Bring to a boil and let it bubble for 30 to 45 seconds until it turns a caramel color. Remove from heat and let cool completely.

Pat the cod fillets dry with paper towels. Rub the miso mixture all over the fish, coating each fillet evenly. Place the fillets in a glass or ceramic dish, cover tightly with plastic wrap, and refrigerate for at least 6 hours or up to 2 days for deeper flavor.

Preheat your oven to 400°F. Spread the sesame seeds on a plate. Lightly wipe off excess miso from the fillets (do not rinse). Press each fillet into the sesame seeds to coat one side.

Heat the vegetable oil in an ovenproof skillet over medium-high heat. Place the fillets sesame-side down in the hot pan and cook until the sesame seeds are golden and the fish is browned, about 3 minutes.

Flip the fillets carefully and cook for another 2 to 3 minutes. Transfer the skillet to the oven and bake for 5 to 7 minutes, until the fish is opaque and flakes easily with a fork.

While the fish bakes, bring a large pot of salted water to a boil. Cook the soba noodles according to package directions until tender, about 4 to 5 minutes. Drain and rinse under cold water.

In a large bowl, whisk together the toasted sesame oil, rice vinegar, grated ginger, salt, and pepper. Add the drained noodles and toss well to coat. Garnish with sliced green onions.