Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and cook until softened, about 5 minutes. Add the smoked paprika, cumin, chili powder, and black pepper and stir to combine.
Place the pork shoulder pieces in a slow cooker. Pour the vinegar over the pork and sprinkle with brown sugar. Cover and cook on low for 8 hours.
Once cooked through, use two forks to shred the pork into small pieces.
Preheat an outdoor grill to medium-high heat. Grill the shredded pork for 8 minutes or until lightly charred.
Serve on hamburger buns with your favorite toppings.