Warm the toasted sesame oil in a large pot over medium heat, then stir in the garlic and ginger for about 3 minutes. The mixture should smell nutty, warm, and fragrant, with pale garlic that has not browned.

Pour in the chicken stock and soy sauce, then add the green onions and carrots; bring the pot to a boil over high heat before reducing to medium-low for 5 minutes, stirring occasionally. The carrots are ready when they bend easily and the broth has picked up the ginger and scallion aroma.

Add the frozen dumplings directly to the pot and bring the broth back to a boil over high heat; cook for about 4 minutes, stirring gently until heated through. The dumplings should float lightly and look plump, with wrappers that remain intact rather than splitting.

Take the pot off the heat, fold in the spinach, and season with sea salt to taste as the greens wilt for about 4 minutes. The spinach should turn soft and emerald green without becoming stringy.

Ladle the soup into bowls and finish with additional green onion and sesame seeds if using. Serve while the broth is steamy and the dumplings are tender.