Whisk together white miso, sherry vinegar, minced ginger, sliced scallions, and garlic in a small bowl. Set aside.
Clean mussels by soaking in cold water for a few minutes, scrubbing gently, and removing any beards. Discard any mussels that are open before cooking.
Heat oil in a deep, wide pot or Dutch oven over high heat. After 1 minute, add the mussels and cook, stirring, for 1 minute.
Add sake, cover pot, and steam until mussels open (about 4–5 minutes). Discard any unopened mussels.
Remove lid, move mussels to one side of the pot. Add miso mixture to the empty side, stir to incorporate, then toss mussels in the sauce to coat.
Using a slotted spoon, transfer mussels to serving bowls. Spoon broth and sauce over them.
Garnish with freshly ground black pepper and julienned scallions. Serve immediately.