In a large bowl, whisk together the mayonnaise, toasted sesame oil, rice vinegar, soy sauce, freshly grated ginger, and honey. Continue whisking until the dressing is completely smooth and emulsified.
Add the shredded cooked chicken breast to the bowl and toss until every strand of chicken is evenly coated in the sesame ginger dressing.
Fold in the shredded carrots, shelled edamame, and sliced green onions. Mix gently until everything is distributed throughout the salad.
Sprinkle in the toasted sesame seeds and chopped fresh cilantro. Give the salad one more gentle toss to combine.
Cover and refrigerate for at least 20 minutes so the flavors blend together.
Just before serving, scatter the crispy wonton strips over the top and gently fold them through. Serve immediately so the wonton strips stay crunchy. This salad is perfect on its own, in lettuce cups, or stuffed into a soft roll.