Preheat your grill to medium heat.
Brush the cabbage wedges with olive oil and season with salt and pepper.
Grill the cabbage for about 5-7 minutes on each side, or until charred and tender.
In a small saucepan, melt the butter over low heat and sauté the garlic until fragrant.
Drizzle the garlic butter sauce over the grilled cabbage and sprinkle with fresh parsley before serving.