Step 1

Heat oil in a heavy pot over medium. Cook ginger and garlic, stirring often, until slightly golden, about 1 minute. Quickly whisk in miso, then gradually add vinegar, mirin, soy sauce, salt, and 3 cups water, whisking until no lumps remain and increasing heat if needed to maintain a simmer. Whisk in butter and 2 tsp. shichimi togarashi. As soon as butter is melted, reduce heat as needed to maintain a simmer. Add sweet potatoes, cover pot, and cook, until potatoes are just tender, 8–10 minutes. Using a slotted spoon, transfer sweet potatoes to a large platter or rimmed baking sheet.

Step 2

Add mussels to pot, cover, and cook until opened, 1–2 minutes. Using slotted spoon, transfer to platter with sweet potatoes, discarding any mussels that don’t open.

Step 3

Add corn, white and pale green scallion parts, green beans, and shrimp to pot, cover, and cook until shrimp are bright pink and corn and green beans are tender, about 4 minutes. Using slotted spoon, transfer to platter and top with dark scallion greens. Serve boil with lime wedges.