Heat the vegetable oil in a large pot over medium heat.
Add the diced onion, sauté until translucent.
Stir in the minced garlic and ginger, cook briefly.
Add the sliced carrot and continue to cook.
Pour in the broth, soy sauce, and sesame oil.
Stir in red pepper flakes and bring to a simmer.
Add the frozen dumplings to the boiling soup.
Simmer until dumplings are cooked through, about 5-7 minutes.
Finally, stir in the baby spinach or bok choy, and cook until wilted.
Taste and adjust seasoning, then serve garnished with green onions.