In a large pot, heat the vegetable oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Pour in the chicken or vegetable broth and water. Add the soy sauce and sesame oil, bringing the mixture to a gentle simmer.
Carefully add the frozen potstickers to the pot. Allow them to cook for about 8-10 minutes, or until they are heated through and floating to the top.
Add the chopped bok choy and sliced mushrooms to the pot, cooking for an additional 3-4 minutes until the vegetables are tender.
Season the soup with salt and pepper to taste.
Serve hot, garnished with sliced green onions and sesame seeds if desired.