Heat oven to 350ºF and line a medium baking sheet with parchment paper.
Place 8 wonton wrappers on baking sheet and lightly brush with 1 teaspoon of sesame oil. Bake for 7-8 minutes or until golden brown.
In the meantime, stir together ingredients for sauce and divide into 2 bowls. Set one bowl onto a serving plate.
Finely chop chicken into ½ inch cubes. Heat 2 tablespoons of sesame oil over medium heat in a medium skillet. Cook chicken in skillet for 10 minutes or until golden brown. Pour reserved sauce over chicken and stir to coat. Cook 2 minutes longer.
Stir Napa cabbage and cilantro together in a medium mixing bowl. Top each wonton with Napa cabbage mixture, chicken and green onion. Serve with reserved sauce for dipping/drizzling.