Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper or lightly grease a Dutch oven.
Whisk together the olive oil, smoked paprika, garlic powder, onion powder, salt, and pepper in a small bowl until well combined.
Brush the entire exterior and the underside of the cauliflower head thoroughly with the oil and spice mixture.
Place the cauliflower on the prepared baking sheet, cover loosely with aluminum foil, and roast for 30 minutes.
Remove the foil and brush the cauliflower generously with half of the barbecue sauce to coat all surfaces.
Return to the oven uncovered and roast for an additional 15 to 20 minutes until the cauliflower is fork-tender and the sauce is caramelized.
Apply the remaining barbecue sauce, garnish with fresh chopped parsley, and slice into wedges for service.