Whisk barbecue sauce, broth, vinegar, brown sugar, Worcestershire, garlic, onion, paprika, chili powder, salt, and pepper in the slow cooker.
Add chicken and turn to coat in the sauce mixture.
Cover and cook on Low 6–7 hours or High 3–4 hours, until the chicken is very tender.
Transfer chicken to a board and shred with two forks.
Stir cornstarch with water to make a slurry. Whisk it into the cooker juices and cook on High 10–15 minutes until thickened.
Return shredded chicken to the sauce, toss to coat, and let stand 5 minutes before serving.