In a medium bowl, whisk together peanut butter, low-sodium soy sauce, brown sugar or honey, rice wine vinegar, minced garlic, grated ginger, and sriracha sauce. Adjust thickness with water as needed and set aside.

In a large mixing bowl, combine cooked chicken, coleslaw mix, grated carrot, chopped cilantro, and roasted salted peanuts. Drizzle half of the peanut sauce over and toss gently.

Heat the tortillas in the microwave for about 30 seconds to make them pliable.

Lay a warm tortilla flat, add filling in the center, drizzle with peanut sauce, fold sides over filling, and roll tightly.

Slice wraps in half diagonally and serve immediately with extra peanut sauce on the side.