Prepare your ingredients by chopping vegetables into bite-sized pieces for even cooking.
In a large pot over medium heat, sauté minced garlic and grated ginger in 1 tablespoon of oil until fragrant, about 30 seconds.
Pour in the chicken broth and bring it to a simmer. Stir in the sliced carrots and shredded cabbage; cook until tender, about 5 minutes.
Gently add the dumplings to the pot and cook according to package instructions, usually around 5-7 minutes depending on whether they are frozen or fresh.
Stir in soy sauce for flavor enhancement, then drizzle sesame oil just before serving.
Ladle the soup into bowls, garnishing with sliced green onions before serving.