In a medium bowl, whisk together peanut butter, low-sodium soy sauce, brown sugar or honey, rice wine vinegar, and minced garlic and ginger to taste.

In a large mixing bowl, combine cooked chicken, coleslaw mix, grated carrot, and chopped cilantro. Drizzle peanut sauce over the mixture, tossing gently.

Warm tortillas in the microwave on a plate covered with a damp paper towel for about 30 seconds.

Spoon an even amount of filling onto each tortilla. Fold in the sides and roll tightly from the bottom up.

Cut each wrap in half diagonally and serve immediately with any remaining peanut sauce.