Remove the chicken breasts from the refrigerator 10–15 minutes before cooking.
Butterfly each chicken breast to create four evenly sized cutlets.
In a small bowl, combine the smoked paprika, garlic powder, salt, black pepper, and cayenne pepper.
Drizzle the chicken with olive oil and coat evenly with the spice mixture.
Heat a large skillet over medium-high heat.
Cook the chicken for 3–4 minutes on the first side.
Flip the chicken and brush the cooked side generously with BBQ sauce.
Continue cooking for another 3–4 minutes, or until the internal temperature reaches 165°F (74°C).
Transfer the chicken to a cutting board with the BBQ-coated side facing down.
Brush the top with additional BBQ sauce and allow the chicken to rest for 5 minutes.
Slice the chicken into thin strips against the grain.
In a small bowl, whisk together the mayonnaise, sour cream, Dijon mustard, apple cider vinegar, sugar, salt, and black pepper.
In a large bowl, combine the grated carrot, sliced red cabbage, green cabbage, and onion.
Pour the dressing over the vegetables and toss until evenly coated.
Lay each tortilla flat.
Add a layer of spinach down the center.
Top with coleslaw followed by the sliced BBQ chicken.
Fold in the sides and roll tightly to form the BBQ Chicken Wraps.
Slice in half if desired and serve immediately.