Season the beef: Pat cubed chuck roast dry and coat evenly with BBQ rub. Let rest at room temperature 30 minutes for better smoke absorption.
Smoke the beef: Preheat smoker to 275°F. Place cubed chuck roast directly on grates and smoke 2 to 3 hours until bark forms and internal temp reaches 160°F. Use hickory, oak, or pecan wood.
Braise in Dr Pepper BBQ bath: Transfer smoked beef to foil pan. Add Dr Pepper, BBQ sauce, brown sugar, and butter slices. Cover tightly with foil. Return to smoker at 325°F and cook 1½ to 2 hours until internal temp reaches 200-205°F. Meat should shred easily.
Shred the beef: Remove from smoker and rest 15 minutes. Using forks, shred beef directly in pan and mix with braising liquid. Taste and adjust seasoning if needed.
Make jalapeño cream cheese spread: Combine softened cream cheese, sour cream, diced jalapeños, caramelized onions, garlic paste, and salt. Mix until smooth and creamy. Refrigerate 15 to 20 minutes.
Assemble sliders: Preheat oven to 375°F. Slice slider rolls in half horizontally. Layer: bottom buns, jalapeño cream cheese spread, pepper jack cheese, shredded BBQ beef, more pepper jack, crispy fried onions, top buns. Optional: brush tops with melted butter or BBQ sauce.
Bake until golden: Cover loosely with foil and bake 15 minutes. Remove foil and bake 5 to 8 more minutes until cheese is melted and tops are golden.