Heat the vegetable oil in a large skillet or sauté pan over medium heat. Add the diced onion and cook for 3-4 minutes until soft and translucent.
Stir in the minced garlic and cook for an additional minute. Then add the mixed vegetables and sauté for 5 minutes until they start to soften.
Pour in the chicken broth, soy sauce, sesame oil, ground ginger, salt, and pepper into the skillet with the sautéed vegetables. Bring to a gentle simmer.
Carefully add the frozen chicken dumplings, ensuring they are submerged in the broth. Cover the pan with a lid and let it simmer for 10-12 minutes.
Remove the lid and let it cook for an additional 2-3 minutes to reduce the broth slightly. Garnish with sliced green onions before serving.