01 - Heat olive oil in a large skillet over medium heat. Add onion and sauté for 3 minutes until softened. Add garlic and cook for 1 minute more until fragrant.
02 - Add chicken breasts, smoked paprika, salt, and pepper to the skillet. Pour in chicken broth. Cover and simmer over low heat for 20 to 25 minutes until chicken is cooked through and tender.
03 - Remove chicken from skillet and shred using two forks. Return shredded chicken to pan, add barbecue sauce, and stir to coat. Simmer uncovered for 5 minutes, allowing sauce to thicken and flavors to meld. Remove from heat.
04 - In a large bowl, combine green and red cabbage, grated carrot, mayonnaise, apple cider vinegar, Dijon mustard, and sugar. Season with salt and pepper, toss well to coat. Refrigerate until ready to serve.
05 - Lightly butter or oil the inside of each bun and toast in a skillet or under broiler until golden brown and crispy.
06 - Pile pulled chicken onto bottom half of each bun. Top generously with slaw, then finish with top bun. Serve immediately while buns are warm.