Miso Soup with Napa Cabbage and Udon

Name: Miso Soup with Napa Cabbage and Udon
Ingredients: 1 cup sliced dried shiitake mushrooms (about 1/2 ounce); 2 cups boiling water; Kosher salt; 1 tablespoon vegetable oil; 1/2 medium yellow onion, thinly sliced; 1 tablespoon peeled and finely chopped fresh ginger (from about a 2-inch piece); 2 medium garlic cloves, finely chopped; 6 cups low-sodium vegetable or chicken broth or stock; 2 tablespoons soy sauce; 1 (12-ounce) package udon noodles; 1/2 medium napa cabbage (about 12 ounces), cored, halved lengthwise, and cut crosswise into 1-inch pieces; 1/2 cup white miso; 4 large eggs (optional); Togarashi, for serving (optional; see What to Buy note)