Remove ham from refrigerator 1 hour before cooking to bring to room temperature. Pat dry with paper towels.
Using a sharp knife, score the surface of the ham in a diamond pattern, cutting about 1/2 inch deep. This helps the glaze penetrate the meat.
Rub the entire ham with olive oil to help develop a beautiful crust.
For smoker method: Preheat smoker to 225 degrees F using apple or cherry wood. Place ham on smoker and cook for 5-6 hours until internal temperature reaches 165 degrees F.
For oven method: Preheat oven to 275 degrees F. Place ham on a rack in a roasting pan with 1 cup apple juice in the bottom. Cover loosely with foil and cook for 4-5 hours.
While ham cooks, prepare the glaze by combining brown sugar, Dijon mustard, apple cider vinegar, garlic powder, cloves, and black pepper in a small saucepan. Heat over medium, stirring until sugar dissolves. Set aside.
When ham reaches 165 degrees F internal temperature, increase smoker to 300 degrees F (or remove foil for oven method). Brush generously with glaze.
Continue cooking, basting with glaze every 20-30 minutes, until internal temperature reaches 200-205 degrees F and a probe slides into the meat with no resistance. This typically takes 1-2 additional hours.
Remove ham from heat and let rest for 30 minutes. The bone should be loose and ready to pull away.
Remove the bone and any excess fat. Using two forks or meat shredding claws, pull the ham apart into bite-sized strands.
Toss the shredded ham with any accumulated pan juices and remaining glaze. Serve warm on slider buns, crusty bread, or as a main dish.