Peel ginger, then slice into very thin strips. Peel garlic and crush with the flat side of your knife. Peel and julienne carrots. Thinly slice scallions, reserving the green parts for serving.
Add toasted sesame oil to a pot over medium heat. Add garlic, scallion whites, and ginger and fry, stirring constantly, until fragrant and softened, approx. 3 min. Add carrots to the pot and fry for approx. 1 min. more. Add water and bring to a boil. Once boiling, add shiitake mushrooms and reduce heat to medium. Let simmer for approx. 5 min.
Season with soy sauce, and a pinch of salt and sugar. Add dumplings and simmer approx. 5 min. more if frozen, and approx 2 min. if room temperature, with the lid half on, until dumplings are cooked through. Dissolve the miso paste in a little of the broth, then add to the pot and stir through. Garnish with the scallion greens and more sesame oil, if desired. Serve immediately and enjoy!
