In a bowl, combine the chicken pieces with the stir fry sauce, sesame ginger dressing, soy sauce, and brown sugar. Let the chicken marinate for at least 30 minutes.

In a deep frying pan, heat enough vegetable oil to be at least 2 inches deep over medium high heat until it reaches 350°F (175°C). Gently fold each wonton wrapper into a triangle shape without sealing the edges. Fry until crispy and golden brown, flipping halfway through. Transfer to a paper towel lined plate to absorb excess grease.

In a bowl, combine the thinly sliced cabbage, shredded carrot, and sesame ginger dressing until thoroughly mixed. Cover and refrigerate until ready to use.

Heat 2 tablespoons of vegetable oil in a non-stick pan over medium-high heat. Add the marinated chicken and cook until fully cooked through and caramelized with the marinade.

Place approximately 1-1 ½ tablespoons of the cooked chicken mixture into each wonton shell. Top the chicken with the coleslaw mixture. Garnish with fresh cilantro leaves and serve with lime wedges.