Place a large soup pot over medium heat and add the toasted sesame oil.
Once the oil is warm, add the minced garlic and fresh ginger. Cook for about 2–3 minutes, stirring frequently, until fragrant. Keep the heat moderate so the garlic does not burn.
Pour in the chicken stock. Add the low-sodium soy sauce, sliced green onions, and julienned or shredded carrots.
Increase the heat and bring the broth to a boil.
Once boiling, reduce the heat to medium-low. Let the broth simmer for approximately 5 minutes, stirring occasionally, until the carrots begin to soften.
Add the frozen dumplings directly to the broth. There is no need to thaw them first unless the package instructions specifically recommend doing so.
Increase the heat and bring the Easy Dumpling Soup back to a gentle boil. Cook the dumplings according to their package directions, approximately 4–6 minutes depending on their size and filling. Make sure any meat-filled dumplings are thoroughly cooked.
Gently stir the soup occasionally while the dumplings cook. Avoid vigorous stirring, which can cause delicate dumpling wrappers to tear.
Once the dumplings are cooked through, remove the pot from the heat.
Add the fresh spinach and gently stir it into the hot broth. Let it sit for 2–4 minutes, or until the spinach has wilted.
Taste the broth before adding additional salt. Both chicken stock and soy sauce can already contain significant amounts of sodium.
Divide the soup between serving bowls. Garnish with additional sliced green onions and sesame seeds, if desired.
Serve immediately while the broth is hot and the dumplings are tender.