Marinate the chicken with soy sauce, fish sauce, lime juice, garlic, and ginger for at least 30 minutes.
Cook the marinated chicken in a grill pan or skillet for about 6-7 minutes on each side until fully cooked.
Prepare the Asian slaw by mixing cabbage, carrots, bell pepper, green onions, and cilantro in a bowl. Whisk together rice vinegar, sesame oil, honey, salt, and pepper in another bowl, then combine with the vegetables.
Assemble the wrap by spreading peanut sauce on a tortilla, adding chicken slices and Asian slaw, then rolling it tightly.