Prep veggies and aromatics: slice mushrooms, carrots, and green onions; grate ginger and mince garlic.
Warm sesame oil in a large pot over medium heat.
Sauté ginger and garlic until fragrant, about 30 seconds.
Add mushrooms and carrots; cook until slightly softened, 2 to 3 minutes.
Pour in chicken broth, soy sauce, and rice vinegar; bring to a gentle boil.
Slide in frozen potstickers; simmer until they float and are heated through, 5 to 7 minutes.
Stir in spinach and green onions; cook until wilted, about 1 minute.
Season with white pepper, red pepper, and a pinch of salt. Thin with water if desired.
Ladle into bowls. Finish with sesame seeds and a drizzle of chili oil.