Rinse the cabbage and remove any damaged or dark pieces to the outer edge of the cabbage. Slice the cabbage into 1/2 inch, circular slices. Place one slice of the cabbage onto a 12 inch by 12 inch tinfoil square. Place a tablespoon of butter into the center of the cabbage. Sprinkle the entire cabbage with salt and pepper. Wrap the tinfoil around the circle piece of cabbage to seal the edges and top. Continue to do this with all slices of cabbage (you should have about 8).
Heat an outdoor grill to medium-high heat. Place the tinfoil wrapped cabbage onto the grill. Close the grill lid and cook for 5 minutes. Turn the cabbages to the other side and grill on that second side for another 5-10 minutes. You can check the cabbage mid way through to see if the cabbage is tender and slightly charred.
When the cabbage is finished cooking, remove from the grill and let the cabbage sit to cool for 5 minutes. You can serve the cabbage right from the tinfoil or transfer to a plate. You can top the cabbage with balsamic vinegar, crumbled feta or blue cheese and/or crumbled bacon. Or, just enjoy plain with the butter, salt and pepper.