Soba and Sweet Potatoes in Miso Lime Broth

Name: Soba and Sweet Potatoes in Miso-Lime Broth
Ingredients: 2 tablespoons extra-virgin olive oil; 1 tablespoon freshly grated ginger; 4 scallions, whites and greens separated and thinly sliced; 3 cloves garlic, minced; 4 ounces shiitake mushrooms, trimmed and thinly sliced; 1 sweet potato, peeled and diced; 4 ounces soba or other buckwheat noodles; 2 heads baby bok choy, sliced in 1/2-inch pieces; 1/2 cup sweet white miso; 1 tablespoon fresh lime juice, plus lime wedges for serving; Kosher salt