Preheat the oven to 425°F (220°C) and line a large rimmed baking sheet with parchment paper.
Place the cabbage wedges on the prepared baking sheet in a single layer, ensuring they are not overlapping.
Drizzle the olive oil evenly over the cabbage wedges, then use a pastry brush or your hands to coat them thoroughly.
Sprinkle the salt, black pepper, and smoked paprika evenly over the cabbage wedges, flipping them to ensure both sides are seasoned.
Roast the cabbage in the preheated oven for 25-30 minutes, flipping the wedges halfway through, until they are tender and the edges are caramelized and slightly crispy.
Remove the cabbage from the oven and drizzle with apple cider vinegar just before serving.