Heat up your grill to medium heat and remove the outer protective leaves from the cabbage-- just the first layer or so that splay open. Then, slice your cabbages into discs through the center core, keeping the core intact. At the very end, we'll remove it, but it'll help keep the cabbages together on the grill.
You pick-- you can either put the cabbages right on the grill, or if they're having trouble staying together or you'd like to avoid char marks, then get out some tinfoil.
If you're using the spice rub, then mix it all together in a wide flat bowl or a sheet pan large enough for the circumference of the cabbage. Kiss the side of each piece of cabbage into the rub gently, to get a nice thin coating. Depending on how much cabbage you have, you might need to double or triple the rub recipe.
If you're putting them directly on the grill, then get your grill a little greasy first-- a light spray of oil, or brush an oil-dipped rag over the grill quickly and carefully. You need a fatty coating to protect the veggies and help them move easily when flipped. Once the cabbage discs are on the grill, paint on a little olive oil and some salt and pepper on the top if you aren't using the rub. Check the underside often to see how it's cooking. When you flip them, olive oil salt and pepper again if not using the rub. You want the cabbage to get soft and change from bright green to a mellower color.
If you're using tinfoil, then wrap the cabbage slices up carefully after coating them in the rub or just oil-salt-pepper on both sides, and place on a medium-hot grill for 20 minutes, flipping once, and allow them to steam in their packages.
After removing from the grill allow to rest for 2-3 minutes, and then making broad chops, cut into 2-3 inch pieces, removing the tough core as you work and discarding. Taste, adjust seasoning (if you didn't use the rub and want to amp up the flavor, try splashing on a simple vinaigrette made from honey, apple cider vinegar, salt and pepper and some sunflower oil, 4 - 1 - 0.5 oil to vinegar to honey.)