Preheat Oven: Preheat oven to 325°F (160°C).
Prepare the Pork Shoulder: Pat the pork shoulder dry with paper towels. Score the fat in a crisscross pattern (optional) to help render fat and crisp the crust.
Make the Garlic-Rosemary Rub: In a small bowl, mix minced garlic, chopped rosemary, olive oil, salt, pepper, and paprika.
Apply the Rub: Rub the mixture evenly over the pork shoulder, pressing gently to adhere. Optional: Marinate for 2–4 hours or overnight in the refrigerator for deeper flavor.
Prepare Roasting Pan: Place pork shoulder on a rack in a roasting pan. Add chicken broth to the pan to keep the meat moist. Optionally, scatter onion quarters and rosemary sprigs around the pork.
Roast the Pork: Roast in preheated oven for about 3–4 hours, or until internal temperature reaches 190°F (88°C) for pull-apart tenderness. Baste occasionally with pan juices to maintain moisture.
Rest the Meat: Remove from oven and tent loosely with foil. Let rest for 15–20 minutes before slicing.
Slice and Serve: Slice the pork shoulder or shred it for sandwiches. Serve with pan juices drizzled over top.