In a small bowl, combine the brown sugar, salt, paprika, cumin, garlic powder, onion powder, and black pepper until well blended.

Trim any excess fat from the pork butt, leaving some fat intact for flavor. Pat the pork dry with paper towels, then cut it into 3 to 4-inch chunks. Generously rub the spice mixture all over the pork chunks, pressing it into the meat. For best results, you can do this step up to 24 hours in advance and refrigerate the seasoned pork.

Set your oven to 300°F and position a rack in the lower third of the oven.

Heat oil in a Dutch oven over medium-high heat until shimmering. Working in batches to avoid crowding, sear the pork chunks until browned on all sides, about 2-3 minutes per side. Be careful, as the sugar in the rub can burn quickly.

Pour the Coke and chicken stock around (not over) the pork to keep the seasoned crust intact.

Cover the Dutch oven with its lid and place it in the preheated oven. Cook for 3 hours.

After 3 hours, remove the lid and continue cooking for another 1-2 hours, or until the pork is very tender and easily pulls apart with a fork. The internal temperature should reach about 205°F for perfect pulling consistency.

Remove the Dutch oven from the oven and let the pork rest for about 20-30 minutes. Transfer the pork to a cutting board and shred with two forks, discarding large pieces of fat.

Skim excess fat from the Dutch oven's cooking liquid. Return the shredded pork to the pot and toss with the reduced liquid to moisten and flavor the meat. Taste and adjust seasoning if needed.

Serve as is with the flavorful cooking liquid or toss with your favorite BBQ sauce for a more traditional pulled pork experience.