Cold coming on? This aromatic broth, brimming with vegetables, is just the fix.
In a medium pot, heat oil over medium heat. Add ginger, scallion whites, and garlic and cook until fragrant, about 2 minutes. Add shiitakes and cook until tender, about 2 minutes. Add sweet potato and toss to coat. Add 6 cups water and bring to a boil, then reduce heat and simmer until sweet potatoes are tender, 6 to 8 minutes.
Meanwhile, cook soba according to package instructions. Drain and rinse well with cold water. Set aside.
Add bok choy to soup and cook until tender, about 2 minutes. Stir in cooked soba.
Remove 1 cup hot broth and whisk with miso until smooth, then stir into soup. Add lime juice and season with salt. Serve with scallion greens and lime wedges.