Cut the cabbage into quarters, leaving the core intact to hold the wedges together. This prevents the leaves from falling apart during grilling.
In a small bowl, combine the olive oil, minced garlic, salt, and black pepper. Brush the cabbage wedges evenly with this mixture.
Preheat the grill to medium-high heat. Place the cabbage wedges on the grill grates and cook for 4-5 minutes per side, or until golden brown grill marks appear.
Meanwhile, in a small saucepan, warm the BBQ sauce with the honey until slightly thickened and the flavors meld together.
Once the cabbage is cooked, brush it with the warm BBQ sauce and sprinkle with toasted sesame seeds before serving.
Serve immediately while hot, as a side dish to grilled meats or other vegetables, or on its own as a light, flavorful dish.
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