Slice the pork shoulder into medium-thick slices. Season with salt, pepper, and smoked paprika, then rub in the crushed garlic.
Coat the meat with BBQ sauce and let it marinate for at least 30 minutes to allow the flavors to meld.
Preheat the oven to 350°F (180°C). Place the pork in a baking dish, drizzle with olive oil, and bake for 40 minutes, turning occasionally and basting with more BBQ sauce.
While the pork is baking, prepare the sweet potato mash. Peel the sweet potatoes, dice them, and cook in salted water until tender (about 15 minutes).
Drain the sweet potatoes and transfer them to a large bowl. Add the butter, sour cream, and nutmeg, then mash until smooth using an immersion blender or potato masher.
Season the sweet potato mash with salt to taste, then mix thoroughly to achieve a creamy consistency.
Serve the juicy BBQ pork shoulder with the warm sweet potato mash, and sprinkle with fresh, chopped parsley.
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