Ingredients

  • 2 heads of garlic, halved crosswise
  • 1/4 cup extra-virgin olive oil, plus more for drizzling
  • Kosher salt
  • Pepper
  • 1 tablespoon minced thyme
  • 2 teaspoons dry mustard powder
  • 2 teaspoons sweet paprika
  • 2 teaspoons finely grated peeled fresh ginger
  • 1 teaspoon finely grated orange zest
  • One 5-pound, bone-in pork butt (shoulder roast)
  • 1/4 cup light brown sugar
  • 1/4 cup distilled white vinegar
  • 1/4 cup apple cider vinegar
  • 1 1/4 cups ketchup
  • 1 cup cola
  • 1/4 cup apple cider vinegar
  • 1/4 cup cayenne pepper hot sauce, such as Franks Red Hot
  • 2 tablespoons unsulfured molasses
  • 2 tablespoons cornstarch
  • Split potato buns, Red-and-Green Coleslaw and Habanero Vinegar, for serving

Method

  • Make the Pork Preheat the oven to 350.
  • Arrange the garlic cut side up on a sheet of foil, drizzle with oil and season with salt and pepper.
  • Wrap the garlic in the foil and roast for about 1 hour, until very soft.
  • Let cool, then squeeze the garlic cloves out of the skins into a medium bowl.
  • Add the thyme, mustard powder, paprika, ginger, orange zest and the 1/4 cup of oil and mash into a paste.
  • Reduce the oven temperature to 300.
  • Set a rack in a flameproof medium roasting pan and put the pork on it.
  • Season the pork with salt and pepper, then rub it all over with the garlic paste.
  • Cover with foil and roast for 6 hours, until an instant-read thermometer inserted in the thickest part of the meat registers 200; uncover for the last 45 minutes of cooking.
  • Transfer to a work surface and let cool, then shred.
  • Discard the fat and bones.
  • Spoon off all but 2 tablespoons of fat from the roasting pan.
  • Add the sugar, both vinegars and 1/2 cup of water to the pan and cook over moderately high heat, whisking, until bubbling and the sugar dissolves, 5 minutes.
  • Add the pork and toss to coat.
  • Season the pork generously with salt and pepper and toss again; keep warm.
  • Meanwhile, make the Sauce In a saucepan, whisk the ketchup, cola, vinegar, hot sauce, molasses and cornstarch and bring to a boil.
  • Simmer over moderate heat, stirring, until glossy and thick, 8 minutes; keep warm.
  • Pile the pork on the buns and top with the barbecue sauce and coleslaw.
  • Close the sandwiches and serve, passing the habanero vinegar at the table.