Shred the cooked chicken, shred the cabbages, grate the carrot, and slice the cucumber and green onions. Toast the nuts in a dry skillet over medium heat for 2–3 minutes until fragrant.
Whisk together soy sauce, rice vinegar, sesame oil, honey, garlic, ginger, and neutral oil until emulsified. Taste and adjust sweetness, salt, or tang.
If you want warm chicken, quickly toss shredded chicken in a hot skillet with 1 teaspoon oil for 1–2 minutes until heated through and lightly browned.
In a large bowl, combine cabbages, carrot, cucumber, green onions, cilantro, and chicken. Pour two-thirds of the dressing over and toss to coat. Add more dressing to taste.
Fold in toasted nuts and crispy rice noodles right before serving so they remain crunchy. Sprinkle with sesame seeds and red pepper flakes if desired.
Serve immediately with lime wedges on the side. Store leftovers with dressing separate and add crunchy toppings at serving time.