Make the dressing. In a small bowl, whisk together peanut butter, lime juice, soy sauce, honey, rice vinegar, and sriracha.
Add warm water, a little at a time, until the dressing is smooth and pourable. Stir in sesame oil and a small pinch of salt. Taste and adjust sweetness, heat, and acidity.
Prep the vegetables. Shred the cabbage, julienne the carrot and cucumber, and slice the red bell pepper and green onions.
Chop the cilantro and tear the mint leaves.
Toss the salad base. In a large bowl, combine chicken, cabbage, carrot, bell pepper, cucumber, green onions, cilantro, and mint. Drizzle on about two-thirds of the dressing. Toss until everything is lightly coated but not soggy.
Warm the wraps (optional but helpful). Briefly warm tortillas in a dry skillet or microwave for 10–15 seconds to make them flexible.
If using lettuce leaves, pat dry so they don’t tear.
Assemble. Lay out a tortilla or lettuce leaf. Add a generous scoop of chicken salad to the center. Sprinkle with chopped peanuts.
Fold the sides in and roll tightly like a burrito. Repeat with remaining wraps.
Finish and serve. Serve with extra dressing on the side and lime wedges. Add a final squeeze of lime over the top for a bright finish.