Preheat your oven to 300°F (150°C).
Pat the pork shoulder dry with paper towels.
Rub the olive oil, salt, and pepper all over the pork.
In a large skillet, heat the remaining olive oil over medium-high heat.
Sear the pork shoulder on all sides until browned.
Transfer the pork to a roasting pan.
In the same skillet, add onions and garlic, sauté until fragrant.
Stir in chicken broth, smoked paprika, thyme, and brown sugar.
Pour this mixture over the pork shoulder in the roasting pan.
Cover tightly with foil and roast for 4-6 hours, until tender.