Preheat the oven to 275 degrees F.
Thoroughly sprinkle the outside of the pork with black pepper, paprika, salt and white pepper. Heat a large roasting pan over high heat and sear the pork on both sides. Add the garlic, carrots, celery and onions into the pan, and then pour in the vegetable stock and beer. Add the whole black peppercorns and bay leaves, cover and transfer to the oven to cook overnight or for 8 hours.
Let the pork cool in the liquid until cool enough to handle, about 3 hours. Remove the meat from the braising liquid and "pull" to desired texture. Strain the braising liquid into a saucepan and cook until reduced by half, adjusting the flavor with brown sugar. Combine the pork with the reduced braising liquid and serve on toasted sesame seed buns with your favorite BBQ sauce (I prefer my bourbon-fig-molasses sauce), a side of coleslaw (make 1 day ahead) and an ice-cold Green Man ESB.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.