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.
02 - Add chicken breasts, smoked paprika, salt, and pepper to the skillet. Pour in chicken broth. Cover and simmer over low heat for 20–25 minutes, or until the chicken is cooked through and tender.
03 - Remove the chicken from the skillet and shred using two forks. Return shredded chicken to the pan, add barbecue sauce, and stir to coat. Simmer uncovered for 5 minutes, allowing the 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, then toss well. Refrigerate until ready to serve.
05 - Lightly butter or oil the inside of each bun and toast in a skillet or under the broiler until golden.
06 - Pile pulled chicken onto the bottom half of each bun. Top generously with slaw, then finish with the top bun. Serve immediately.