In a large mixing bowl, combine 4 cups thinly sliced Napa cabbage, 2 cups thinly sliced red cabbage1 cup shredded carrots, 1/2 cup sliced green onion, and 2 cups shredded cooked chicken.
Add the 1 (15 ounce can) mandarin oranges in water, 1/4 cup sliced almonds, and 1/4 cup chopped fresh cilantro. Toss to combine.
In a small mixing bowl, whisk together the 1/4 cup soy sauce, 1/4 cup rice vinegar, 2 tablespoons toasted sesame oil, 2 teaspoons minced garlic, 2 teaspoons grated ginger, 1 teaspoon granulated sugar, and 1 teaspoon black pepper until well combined.
Drizzle the dressing over the salad and toss everything together until the dressing is evenly distributed.
Just before serving, top with the 3/4 cup wonton strips and 2 tablespoons sesame seeds.