Prepare the Filling. In a bowl, combine ground chicken, garlic, green onions, soy sauce, sesame oil, and ginger (if using). Mix until well incorporated.
Assemble the Wontons. Place a small spoonful of filling in the center of each wonton wrapper. Brush the edges of the wrapper with the beaten egg and fold in the ends to contain the filling. Press the edges to seal tightly.
Preheat the Air Fryer. Preheat the air fryer to 375°F.
Air Fry the Wontons. Lightly spray the wontons with cooking spray and place them in a single layer in the air fryer basket. Air fry for 8-10 minutes, flipping halfway through, until golden brown and crispy.
Serve. Transfer the crispy wontons to a serving platter and serve with your favorite dipping sauces, such as sweet chili sauce or soy sauce.