Bring the chuck roast to room temperature and pat it dry with paper towels. Coat the surface with mustard or hot sauce, then generously season with your favorite beef seasoning.
Preheat the smoker to 250°F and add a few hickory wood chunks. Place the chuck roast on the smoker and smoke for about 3 hours, or until a deep bark develops.
Combine the mayonnaise, garlic paste, adobo sauce, black pepper, and white vinegar in a small bowl. Refrigerate until ready to use.
Add the onions, pickled jalapeños, chipotle peppers, adobo sauce, Italian seasoning, chili lime seasoning, and garlic powder to a Dutch oven. Place the smoked chuck roast on top.
Pour in the beer, Worcestershire sauce, and beef broth. Return the Dutch oven to the smoker and maintain a temperature between 250–275°F.
Combine the tomatoes, white onion, jalapeño, cilantro, lime juice, and salt in a bowl to make the pico de gallo. Refrigerate until serving.
Check the chuck roast after 2–3 hours of braising. Add a little water if the liquid level becomes too low. Continue cooking until the beef is tender enough to shred.
Transfer the chuck roast to an aluminum pan and shred the meat. Strain the solids from the braising liquid, then return the liquid and shredded beef to the Dutch oven. Cover to keep warm.
Slice and toast the French bread. Spread garlic mayo over both sides, then fill with the shredded beef.
Top with shredded Jack cheese and melt the cheese under the broiler or with a kitchen torch. Finish with pico de gallo and serve