In a large bowl, combine the ground chicken, cabbage, carrots, shiitake mushrooms, green onions, egg, oyster sauce, chicken bouillon, garlic powder, onion powder, sesame oil, salt, and pepper. Mix until everything is evenly combined.
Dip one rice paper wrapper in water for 5–10 seconds until just pliable. Place it on a clean surface.
Spoon about 2 tablespoons of filling into the center. Fold the top and bottom over the filling, then fold in both sides to make a square dumpling. Repeat with the remaining filling.
Lightly spray dumplings with oil.
Air fry at 375°F (190°C) for 12–15 minutes, flipping halfway through and spraying lightly with more oil if needed, until golden brown, crispy, and the chicken reaches 165°F (74°C).
Whisk all the sauce ingredients together in a small bowl. Serve alongside the hot crispy dumplings.
