Miso Soup with Napa Cabbage and Udon

Name: Miso Soup with Napa Cabbage and Udon
Ingredients: 0.5 ounce cup sliced dried shiitake mushrooms (about; 4 large eggs (optional); 1 tablespoon peeled and finely chopped fresh ginger (from about a 2-inch piece); 2 medium garlic cloves, finely chopped; 4 servings Kosher salt; 6 cups low-sodium vegetable or chicken broth or stock; 2 tablespoons soy sauce; 12 ounce package udon noodles; 1 tablespoon vegetable oil; 2 cups boiling water; 0.5 cup white miso; 0.5 medium yellow onion, thinly sliced