Preheat the smoker to a steady 250°F (120°C) about 30 minutes before cooking.

Pat the chuck roast dry with paper towels and trim excess hard fat, leaving a 1/4-inch fat cap.

In a small bowl, combine paprika, brown sugar, black pepper, garlic powder, onion powder, kosher salt, cayenne pepper, and smoked paprika to make the dry rub.

Coat the roast generously with the rub on all sides and let it sit at room temperature for 15 minutes.

Place the roast on the smoker grates fat-cap side up. Insert a meat thermometer probe into the thickest part, close the smoker, and cook undisturbed for 2–3 hours.

Maintain smoker temperature between 245°F and 255°F (118°C–124°C), adding hickory, oak, or pecan wood every hour during the first 3 hours.

When the internal temperature reaches 165°F (74°C), remove the roast, place it on a double layer of aluminum foil, pour 1/2 cup beef broth over the meat, wrap tightly, and return to the smoker.

Continue smoking until the internal temperature reaches 195°F–205°F (90°C–96°C), approximately 2–3 additional hours. Baste with melted butter every 2 hours before the wrap stage if desired.

Remove the wrapped roast from the smoker and let it rest for at least 15 minutes. Unwrap carefully, slice against the grain into 1/4-inch slices, and serve hot.