In a small bowl, mix 1/4 cup BBQ sauce, olive oil, smoked paprika, garlic powder, salt, and pepper. Place chicken breasts in a resealable bag or shallow dish, pour the marinade over, and turn to coat. Let marinate at room temperature for 15 minutes while you preheat the grill.
Preheat grill to medium-high heat (about 400°F). Grill the chicken for 6-7 minutes per side, brushing with additional BBQ sauce during the last 2 minutes of cooking, until internal temperature reaches 165°F. Remove from grill and let rest for 5 minutes before dicing into bite-sized cubes.
In a small bowl or jar, whisk together olive oil, apple cider vinegar, 1 tbsp BBQ sauce, honey, Dijon mustard, smoked paprika, salt, and pepper until emulsified. Set aside.
In a large bowl, combine the black beans, corn, shredded red cabbage, shredded carrots, green onions, and cilantro. Add the diced BBQ chicken. Pour the dressing over the salad and toss gently until everything is evenly coated.
Transfer the salad to a glass container or serving bowl. Garnish with extra cilantro and a drizzle of BBQ sauce if desired. Serve at room temperature or chilled.