Prepare the chicken. Pat the chicken breasts dry with paper towels. In a small bowl mix the smoked paprika, garlic powder, onion powder, black pepper, salt, and chili powder. Rub the olive oil over the chicken and coat evenly with the spice mixture.
Cook the chicken. Heat a skillet or grill pan over medium-high heat. Place the chicken in the pan and cook for about 5–6 minutes per side until golden brown and fully cooked. The internal temperature should reach 74°C (165°F).
Glaze the chicken. Lower the heat slightly and brush the barbecue sauce over both sides of the chicken. Cook for another 1–2 minutes so the sauce becomes slightly sticky and caramelized.
Rest and slice. Remove the chicken from the pan and let it rest for 5 minutes. Slice into thick strips so the wraps stay hearty and juicy.
Prepare the coleslaw. In a medium bowl combine the green cabbage, purple cabbage, and grated carrot. In a separate small bowl whisk together the mayonnaise, yogurt, apple cider vinegar, honey, salt, and black pepper. Pour the dressing over the vegetables and toss until everything is evenly coated.
Warm the wraps. Lightly brush each tortilla with a small amount of olive oil. Heat them in a skillet for about 30–40 seconds per side until warm and slightly toasted but still flexible.
Assemble the wraps. Spread about 1/2 tablespoon of mayonnaise or garlic sauce across the center of each tortilla. Add a generous handful of coleslaw followed by several slices of BBQ chicken.
Finish the wraps. Drizzle a small spoonful of extra barbecue sauce over the chicken and sprinkle chopped parsley for freshness.
Wrap and serve. Fold in the sides of the tortilla, roll tightly from the bottom, and slice in half if desired. Serve immediately while the wraps are warm and the coleslaw is crisp.
