Pat the pork shoulder dry with paper towels. Rub the pork all over with olive oil.
3-4 pounds pork shoulder, 1 tablespoon extra virgin olive oil
In a small bowl, combine the brown sugar, smoked paprika, salt, pepper, chili powder, garlic powder, onion powder, cayenne, cumin, and dry mustard. Coat the pork thoroughly with the rub, pressing it into all sides.
Place the pork in the slow cooker. In a liquid measuring cup, whisk together the apple cider vinegar, chicken broth, Worcestershire sauce, honey, and hot sauce, if using. Pour the mixture around the pork, not directly over the top so the rub stays intact.
1/2 cup apple cider vinegar, 1/4 cup chicken broth, 1 tablespoon Worcestershire sauce, 1 tablespoon honey, 1 teaspoon hot sauce
Cover and cook on low for 8-10 hours or on high for 5-6 hours, until the pork is very tender and easily shreds with a fork.
Transfer the pork to a large bowl or cutting board. Let it rest for 5 minutes, then shred using two forks, discarding excess fat. Return the shredded pork to the slow cooker and toss with a few spoonfuls of the cooking liquid to lightly coat.
Taste and add additional cooking liquid if desired.
Serve on hamburger buns with coleslaw and pickled red onions.