Heat the olive oil in a large pot over medium heat. Add the onions and garlic and cook until softened, about 5 minutes. Add the pork cubes and cook until lightly browned. Stir in the brown sugar, smoked paprika, cayenne pepper, garlic powder, onion powder, ground cumin, and chili powder.
Add 1 cup of water to the pot and bring to a boil. Reduce heat to low and simmer for 1 1/2 hours or until pork is tender.
Remove from heat and use two forks to shred the pork. Stir in the BBQ sauce and serve on hamburger buns.