Preheat the oven to 350 degrees F. Rinse and dry the pork shoulder.
Mix together the brown sugar, garlic, cumin, salt, and cayenne. Rub the mixture generously and evenly over the pork shoulder.
In a large roasting pan or Dutch oven, add the chopped onions, broth, and cola. Place the seasoned pork in the Dutch oven and roast for 4 to 6 hours, checking the pork every hour for tenderness and liquid level.
When the pork is tender enough that it is falling apart, shred it with a fork. Reserve the juices and pour them over the shredded pork before serving.