1) Place the chicken breasts between sheets of waxed or parchment paper and gently pound to a ½-inch thickness. Be careful not to pound them too thin; just enough so that they are the same thickness for uniform cooking. If your chicken breasts are fairly even in thickness, you can skip this step.
2) Combine olive oil and seasonings in a large Ziploc bag or bowl. Stir to mix. Add chicken breasts and shake or stir until all of the chicken is well-coated. Place the chicken in the refrigerator for 10 to 20 minutes while preparing the salad dressing.
3) Place the bell pepper and cilantro leaves in a blender or the work bowl of a food processor. Add the remaining ingredients except for the olive oil. Process until smooth, about 30 to 60 seconds.
4) With the blender or food processor running, add the olive oil in a thin stream and continue processing for 1 minute after all of the oil has been added. Store the dressing covered in the refrigerator.
5) If you have a hot grill available, grill the chicken for 3 to 4 minutes on each side. Do not overcook. If no grill is available, preheat the oven to 350 degrees Fahrenheit and bake your chicken in a pan for about 30 minutes. The internal temperature should be 165 degrees, Fahrenheit. Let the chicken sit for 5 minutes to redistribute the juices before you cut it into ½-inch cubes; let cool.
6) Increase the oven temperature to 375 degrees. Lay the wontons out over a large greased baking sheet. Then spray a thin layer of oil over the tops of all the wontons with an oil mister filled with oil (or nonstick spray). Place on the oven rack and bake until golden brown, for about 5-10 minutes. As they cool, they become crispy. Repeat this process for more crunchy wontons to add to your salad. Break the wontons into bite-sized pieces.
7) If using thin rice sticks (rice threads), pull them apart as you spread them out on the prepared baking sheet. Use the same baking method as with the wontons except cook them for longer until crisp but tender. They aren’t as good as the deep fried version, but they give the a salad needed crunch if you can’t use the wontons. This healthy version of wontons is actually better than the deep fried version, so that is why I opt for the baked wantons.
8) Place the Napa and red cabbage, carrots, scallions, cucumber, and edamame into a very large mixing bowl and toss to mix. Add the chicken cubes to the mixing bowl. Keep refrigerated until ready to serve. Add the peanuts and diced avocado just prior to serving. Use a squeeze bottle or syrup dispenser to drizzle the dressing over the salad and top with the broken wontons pieces. Serve immediately.