North Carolina-style pulled pork sandwiches served on potato rolls with a vinegar-based barbecue sauce and quick coleslaw.
Working ahead, sprinkle the pork shoulder all over with sea salt. Refrigerate for at least 2 hours up to one day.
Heat a large dutch oven, or other large, heavy bottomed pot, over medium-high heat. Add the olive oil and shallots and saute for 2 minutes. Next add the pork shoulder. Sear on all sides, until you've achieved a nice color all around (this will take about 12 minutes). Pour in the wine, and add 1/2 teaspoon salt, peppers, paprika, bay, and honey. Bring liquid to a quick boil, and then turn heat to low, and cover.
Continue to cook over low heat for 4 - 8 hours. Flip the meat occasionally, and check the liquid levels – the liquid should cover roughly half of the meat. If the liquid runs low, add a bit of wine, water, or vinegar. Remove from heat when meat is tender and starting to fall apart – the longer it cooks, the more tender it will be.
Place on a carving board, trim any remaining fat, and then use the tips of tongs to pull the pork apart. Place back in the cooking liquid, bring heat back up, and warm. Serve with a slotted spoon.
To make the barbecue sauce, combine all of the ingredients in a small sauce pan. Bring to a boil, and then turn heat to low. Cook 20 minutes. Remove from heat, and allow the flavors to mature, anywhere from 30 minutes to 4 hours.