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 already 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/stir until well-coated. Place chicken in refrigerator for 10 to 20 minutes while preparing salad dressing.
3) Place 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 until 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. Otherwise, preheat oven to 350 degrees F and bake your chicken in a pan for about 30 minutes. The internal temperature should be 165 degrees F. Let 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 use nonstick spray). Place on 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 into bite-sized pieces. (This healthy version of wontons is actually better than the deep fried version.)
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 salad a needed crunch if you can’t use the wontons.)
8) Place the Napa and red cabbage, carrots, scallions, cucumber, and edamame into a very large mixing bowl and toss to mix. Add 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 dressing over the salad, and top with broken wonton pieces. Serve immediately.