Prepare the chicken: Season chicken breasts with salt and black pepper. Place in the crock of a 5- or 6-quart slow cooker.
Add ingredients: Pour in chicken broth, then add chopped celery, cream cheese, hot sauce, minced jalapeno, and 4 oz. of crumbled blue cheese.
Cook: Cover and cook on high for 3–4 hours or low for 6–7 hours.
Shred the chicken: About 30 minutes before serving, remove the lid and shred the chicken using two forks. Stir in shredded mozzarella cheese until fully combined and melted.
Finish and garnish: Return the lid, keep warm, then remove lid before serving. Garnish with remaining blue cheese, sliced green onions, and sliced jalapeno if desired.
Serve: Pair with celery stalks and carrot sticks—or crackers, if you prefer.