Preheat the oven to 400ºF. Line a large baking sheet with parchment paper.
Cut the cabbage into quarters, then cut each quarter in half, yielding 8 wedges. Leave the core intact, as this will help the wedges hold their shape.
Place the wedges on the baking sheet and brush both sides with olive oil. Sprinkle with salt and pepper. Roast the wedges, cut sides down, for 20 minutes. Flip the wedges and roast for another 15-20 minutes or until fork tender and lightly browned.
While the cabbage roasts, melt the butter in a small pot over low medium. Add the garlic. Stir constantly until the butter and garlic turn golden brown, about 5 minutes.
To serve, brush the brown butter over the cabbage wedges, sprinkle with parsley, and serve.