1 pork roast (3 to 4 lb), preferably pork shoulder or Boston butt
1 tablespoon olive oil
3 tablespoons paprika
1 tablespoon kosher salt
1 tablespoon granulated sugar
1 tablespoon brown sugar
1 tablespoon ground cumin
1 tablespoon chili powder
1 teaspoon cayenne pepper
freshly ground pepper
1 tablespoon corn oil
1 small yellow onion, finely chopped
2 cloves garlic, thinly sliced
1 1/2 cups tomato sauce
3/4 cup cider vinegar
1/2 cup firmly packed brown sugar
2 tablespoons chili powder
1 tablespoon Dijon mustard
dash of hot-pepper sauce
16 slider rolls or 8 hamburger rolls, split
Pat the pork dry and brush with the olive oil.
To make the dry rub, in a small bowl, stir together the paprika, salt, sugars, cumin, chili powder, cayenne, and black pepper to taste. Rub the dry rub all over the pork, wrap in plastic wrap, and let marinate in the refrigerator for at least 4 hours or up to overnight.
Preheat the oven to 300°F/150°C/gas. Put the pork on a rack in a large roasting pan/tray and roast until an instant-read thermometer registers 170°F/80°C, about 6 hours.
To make the barbecue sauce: Heat the oil in a saucepan over medium heat. Add the onion and garlic and sauté until softened and golden, about 5 minutes. Add the ketchup/tomato sauce, vinegar, brown sugar/demerara sugar, chili powder, mustard, and hot-pepper sauce and stir to mix well. Simmer gently, stirring occasionally, until the sauce thickens and the flavors blend, 20 to 25 minutes. Taste and adjust the seasoning, if necessary.
Remove the pork roast from the oven and transfer to a cutting board or large platter. Tent loosely with aluminum foil and let rest for 15 to 20 minutes. “Pull” the pork apart with 2 forks to form shreds and transfer to a large bowl. Add the sauce to the shredded pork.
To serve, spoon the pulled pork onto the bottom halves of the slider or hamburger rolls, dividing it evenly. Replace the tops of the buns; if using regular hamburger rolls, cut each sandwich in half. Serve at once.