In a large pot, heat the vegetable oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Pour in the chicken or vegetable broth, soy sauce, fish sauce, and sesame oil. Bring the mixture to a gentle boil.
Add the julienned carrots, snap peas, and sliced mushrooms to the pot. Reduce the heat and let simmer for about 5 minutes until the vegetables are tender.
Carefully add the frozen potstickers to the pot and cook according to package instructions, usually about 5-7 minutes.
Once the potstickers are heated through, stir in the baby spinach and cook for an additional 1-2 minutes until wilted.
Serve the soup hot, garnished with sliced green onions and fresh cilantro. Offer lime wedges on the side for squeezing over the soup.