Preheat and Season: Preheat your oven to 300°F (150°C). Mix the paprika, salt, pepper, garlic powder, onion powder, brown sugar, and cayenne pepper in a small bowl. Rub the spice mixture all over the pork butt.
Sear the Meat: In your cast-iron skillet, heat the olive oil over medium-high heat. Sear the pork butt on all sides until it's nicely browned.
Slow Cook: Place the pork butt on a roasting rack inside the skillet or pot. Pour the broth into the bottom. Cover with a lid (or tightly sealed foil). Slow cook in the preheated oven for approximately 4-5 hours or until the meat reaches an internal temperature of 195-205°F (90-96°C).
Rest and Serve: Remove the pork butt from the oven and let it rest for 15-20 minutes. Then, shred the meat using two forks. Serve with your favorite sides like coleslaw, buns, or rice.