1. In a bowl, combine the smoked chipotle, adobo sauce, minced garlic, smoked paprika, ground cumin, dried oregano, salt, black pepper, and vegetable oil to make a marinade for the beef.
2. Place the braising steak in a large dish and rub the marinade all over it, ensuring it is well-coated. Cover the dish with plastic wrap and let it marinate in the refrigerator for at least 2 hours (overnight for more intense flavour) if time permits.
3. Preheat your smoker to a temperature of around 225°F (110°C). Add your preferred wood chips for smoking, such as hickory or mesquite, to infuse the meat with a smoky flavour.
4. Remove the beef from the marinade and pat it dry with paper towels. Place the roast directly on the smoker rack and close the lid. Smoke the beef for 3-4 hours or until it reaches an internal temperature of around 165°F (74°C).
5. While the beef is smoking, prepare the birria sauce. In a blender or food processor, combine the beef broth, diced tomatoes, chopped onion, minced garlic, smoked chipotle, adobo sauce, tomato paste, apple cider vinegar, dried oregano, ground cumin, smoked paprika, salt, and black pepper. Blend until smooth.
6. Transfer the birria sauce to a large pot or Dutch oven. Bring it to a gentle simmer over medium heat, then reduce the heat to low and let it cook for 2-3 hours, allowing the flavours to meld together and the sauce to thicken slightly.
7. Once the smoked beef chuck roast is done, remove it from the smoker and let it rest for a few minutes. Shred the beef using two forks or your hands, discarding any excess fat or connective tissue.
8. Add the shredded beef to the pot with the birria sauce. Stir well to coat the meat in the flavourful sauce. Let it simmer for another 20-30 minutes, allowing the beef to soak up the sauce.
9. Warm the corn tortillas on a skillet or griddle until soft and pliable.
10. To assemble the tacos, place a spoonful of the beef birria in the center of each tortilla. Top with shredded mozzarella cheese, chopped onion, and cilantro. Squeeze some lime juice over the filling.
11. Serve the Smoked Chipotle Beef Birria Tacos immediately with extra birria sauce on the side for dipping and lime wedges for an extra burst of citrus flavour.

Enjoy the smoky, spicy goodness of these Smoked Chipotle Beef Birria Tacos with your family and friends!