Cut the cabbage into two halves through the core, but make sure that the core stays intact. Next, cut each of those halves into quarters, but make sure that the core is equally attached to each of the wedges. The core is going to hold all the wedges together on the grill. Brush both sides of the cabbage wedges with the extra-virgin olive oil.
Keep the cabbage on the grill until it gets a little charred on the outside. Once the cabbage starts to soften after you've flipped it, remove the cabbage from the grill. It should take 6-8 minutes per side.
In the meantime, you need to whisk the buttermilk, mayonnaise, garlic powder, vinegar, salt, and pepper in a bowl, then add the herbs to the bowl. Mix all the ingredients well and serve the mixture along with the cabbage.