In a large bowl, combine ground chicken, shredded carrots, cabbage, garlic, green onions, hoisin sauce, sesame oil, and one beaten egg.
Place a dumpling wrapper on a clean surface and spoon a teaspoon of filling in the center.
Wet the edges with water and fold into a half-moon, pressing to seal. Crimp edges if desired.
Repeat until all wrappers are filled.
Heat vegetable oil in a non-stick skillet over medium heat.
Add potstickers in a single layer, flat side down. Fry for 2–3 minutes or until bottoms are golden brown.
Carefully add ¼ cup water and cover immediately. Steam for 5 minutes until the filling is cooked through.
Serve hot with soy sauce, Cucumber Salad, or Jalapeño Hot Sauce.