In a large bowl, combine the shredded cabbage, grated carrots, and cooked chicken. Add the chopped green onions, minced ginger, and minced garlic. Drizzle in the soy sauce and sesame oil. Mix everything together until well combined.
Take a potsticker wrapper and place about 1 tablespoon of the filling in the center. Moisten the edges of the wrapper with a little water. Fold the wrapper in half, creating a half-moon shape, and pinch the edges to seal. Repeat this process with the remaining wrappers and filling.
Heat a large pot over medium heat. Carefully add the potstickers to the pot. Cook them for 5-7 minutes, or until they float to the top. Remove them from the pot and set them aside.
In the same pot, pour in the coconut milk and chicken broth. Stir well to combine. Add the lime juice and fish sauce. Bring the mixture to a gentle simmer over medium heat.
Carefully add the cooked potstickers back into the pot with the coconut broth. Let them simmer together for a couple of minutes. Serve in bowls, garnished with fresh cilantro and lime wedges.