Udon Noodle Soup with Miso Broth

Name: Udon Noodle Soup with Miso Broth
Ingredients: 2 tablespoons peanut oil; 6 ounces shiitake mushroom caps, (cleaned and sliced); 3 scallions, (white and green parts separated and chopped); 2 garlic cloves, (minced); 1 teaspoon freshly grated ginger; 6 cups water; 2 cups sliced napa cabbage; 26 ounces frozen udon noodles ((Note 1)); 2 tablespoons white miso paste; 3 tablespoons soy sauce, (or to taste); 1 teaspoon sriracha sauce, (or to taste); 1 teaspoon toasted sesame oil; 1 cup frozen shelled edamame, (thawed); Toasted sesame seeds, (for serving)