Heat the vegetable oil in a large pot over medium heat.
Add the ginger and garlic, sautéing until fragrant, about 1-2 minutes.
Pour in the chicken or vegetable broth and soy sauce.
Bring the mixture to a boil.
Gently add the frozen potstickers to the broth.
Reduce the heat to a simmer and allow cooking according to package instructions, usually 5-7 minutes.
Add the spinach, carrots, and mushrooms, cooking for an additional 2-3 minutes.
Stir in the sesame oil and taste for seasoning.
Serve hot in bowls, garnished with sliced green onions.