For the dressing, combine grated ginger, chopped garlic, rice vinegar, soy sauce, honey, and avocado oil in a small jar. Whisk until well blended and set aside.
For the salad, place chopped romaine in a large bowl. Add red cabbage, green cabbage, carrots, cilantro, green onions, and shredded chicken.
Pour the dressing over the salad and toss gently to coat evenly.
Serve immediately, topped with mandarin oranges, cashews, and almonds as desired.