In a medium bowl, whisk together peanut butter, soy sauce, brown sugar, rice wine vinegar, garlic, ginger, and sriracha until well combined. If too thick, add water to reach a creamy consistency. Set aside.

In a large bowl, combine chicken, coleslaw mix, grated carrot, cilantro, and peanuts. Drizzle with half of the sauce and toss gently. Let sit for 5 minutes.

Wrap tortillas in a damp paper towel and microwave for 30 seconds until warm and soft.

Lay a tortilla flat, add filling, and roll tightly. Repeat with remaining tortillas.

Slice wraps in half and serve with remaining peanut sauce on the side.