Marinate the chicken: In a bowl, combine the Chinese cooking wine, soy sauce, honey, and cornstarch. Add the chicken and mix well. Let it marinate for at least 20 minutes.
Prepare the veggies: Thinly slice the cabbage and radishes. Cut the carrot into matchsticks. Slice the snow peas and green onions. Cut the avocados into large chunks and toss with fresh lemon juice. Leave the mint and cilantro leaves whole.
Cook the chicken: Heat a pan over medium heat and add the marinated chicken. Cook until golden and cooked through, about 5-7 minutes. Remove from the pan and let rest for 5-10 minutes before slicing into chunks.
Make the dressing: In a bowl, combine the grated ginger, peanut butter, honey, soy sauce, lemon juice, and sesame oil. Stir until smooth. Taste and add salt if needed.
Assemble the salad: Assemble right before eating. Combine the veggies (without the avocados), chicken, and herbs in a large bowl. Drizzle with the dressing and toss gently to coat. Top with the avocado and any extra toppings (see recipe tips for more ideas).