In a medium bowl, whisk together peanut butter, soy sauce, brown sugar, rice wine vinegar, garlic, ginger, and sriracha until smooth. Add water if needed for consistency.

In a large mixing bowl, combine chicken, coleslaw mix, carrots, cilantro, and peanuts. Toss gently until well mixed.

Pour the dressing over the filling mixture and toss until coated. Let the mixture rest for 3-5 minutes.

Wrap tortillas in a damp paper towel and microwave for 30 seconds to warm them.

Place a portion of the filling in the center of each tortilla. Fold sides inward and roll tightly from the bottom.

Arrange wraps on a platter and serve with extra peanut sauce and lime wedges.