Trim the out leaves of the cabbage and give them to your neighbor's rabbit. Cut the cabbage in half and then cut each half into 4 wedges ensuring that there is some of the cabbage heart remaining in each wedge.
Mix up the olive oil and lemon juice, place the wedges core side up and drizzle the olive oil and lemon juice mix so that it permeates all the leaves (be generous because it's this moisture that will soften the cabbage). After a good helping of salt and pepper, place the wedges on the grill and give them about 10 minutes on each of the 3 sides of the wedge.
Keep brushing more of the citrus oil on the cabbage throughout the cook process because this will continue to add flavor, keep things moist and stop the outer leaves from burning.