Preheat oven to 300°F / 150°C. Trim excess fat from pork and cut into large pieces to fit in a large Dutch oven.
In a small bowl, combine brown sugar, salt, paprika, garlic powder, onion powder, and cumin, then season with black pepper. Rub all over pork. (This can be done the night before.)
In a large Dutch oven over medium-high heat, heat oil. Working in batches, add pork and sear on all sides. (Spices can burn quickly so don’t let it go for too long!)
Pour the beer around pork, then cover with the lid. Transfer to the oven and cook until pork begins to turn tender about 3 hours. Remove lid and cook until pork is very tender and pulls apart easily with a fork, about 1 to 2 hours more.
Remove pork from Dutch oven and let rest while you prepare the barbecue sauce.