Arrange the sliced onion and green bell pepper in an even layer at the bottom of a 6-quart slow cooker.

Season the beef chuck roast with smoked paprika and black pepper, then place it directly on top of the vegetables.

In a medium bowl, whisk together the barbecue sauce, beef broth, minced garlic, and Worcestershire sauce.

Pour the sauce mixture over the beef roast.

Cover the slow cooker and cook on the low setting for 8 hours (or high for 4 to 5 hours) until the meat is fork-tender.

Remove the beef from the slow cooker and transfer to a cutting board; shred the meat using two forks, removing any large pieces of fat.

Return the shredded beef to the slow cooker and toss with the remaining sauce and vegetables to incorporate.

Toast the buns under a broiler for 1 to 2 minutes until golden.

Portion the beef onto the bottom half of each bun, top with a slice of pepper jack cheese, and place the top bun over the cheese before serving.