Bring the roast to room temperature, 30 to 45 minutes.
Meanwhile, in a small bowl, combine the salt, pepper, espresso powder, garlic powder, chipotle chili powder, and smoked paprika.
Preheat your smoker to 225°F using oak or hickory.
After the roast has come to room temperature, pat it dry then liberally apply the dry rub to the roast, using your hands to press it in so it adheres to the meat.
Place the roast on the center of the grill grate, fatty side up (if applicable). Smoke for approximately 4 hours until the internal temperature registers around 165°F. Remove from the heat and increase the heat to 250°F.
Meanwhile, pour the beef broth and apple cider vinegar in a 9×13-inch baking tray. Place the par-cooked chuck roast in the center of the baking tray and cover very tightly with foil. Place back on the center of the grill and continue cooking the roast until the internal temperature registers to around 200°F, approximately another 3 hours. Remove from the smoker and rest, covered, for 30 minutes before slicing and serving.
Remove from the smoker and keep it covered in the baking dish and let it rest for about 30 more minutes. Transfer the roast to a cutting board and slice.
Serve with some of your favorite barbecue sauce in bowls, sandwiches, or a platter! Enjoy!