Mix together garlic, peppercorns, thyme, and mustard to form a paste; run into the pork shoulder and place it in a roasting pan or slow cooker.
In a separate bowl, mix wine (or juice) and BBQ sauce together; pour it over the pork. Cover roasting pan with a lid or aluminum foil (or if using slow cooker, cover with lid).
For oven, preheat to 350°F (180°C) and cook the pork for 30 minutes; then lower the temperature to 200°F (100°C) and keep cooking for 4 - 5 hours. Pork is done when very tender but not falling apart.
Remove pork from oven and set aside to cool.
Place the remaining liquid from the roasting pan/slow cooker into a small saucepan and heat on stovetop until it thickens into a glaze.
Using two forks shred the pork and place it back into the roasting pan/slow cooker. Stir in the glaze; heating to desire temperature.
Serve pulled pork on buns, with coleslaw on the side.