Put noodles in a bowl with water to cover, and set aside.
Trim mushrooms, and wipe off grit with a damp cloth. Snap off stems, and chop finely. Slice caps thinly, and set aside.
Heat oil in a soup pot. Add scallion whites, mushrooms and carrot, and cook over medium-high heat, stirring frequently, until mushrooms begin to soften, for about 2 minutes.
Add 5 cups water, and bring to a boil. Add edamame, and cook for 4 minutes. Drain noodles, and add to pot with spinach and ginger.
Reduce heat to medium-low, and cook until edamame are tender but still firm, for about 1 minute more. Stir in scallion greens.
Blend 4 tablespoons miso into 1 cup warm water, using a fork to mix. Reduce heat to low, and stir miso into soup, adding more miso for a more intense flavor, if desired.
Add sesame oil and tamari to taste. Serve hot.