Prepare a shallow sheet pan for the smoker—use a disposable one, or cover one from your kitchen in foil. Brush the foil with about one third of the olive oil.

Wash the cabbage and remove just the outer leaves. If necessary, trim the hard stem to flatten the base of cabbage. Set the cabbage on its base (core side down) and cut the rounded edges off the sides. From what remains, cut the head of cabbage into steaks, each about an inch and a half thick.

Transfer the steaks to the prepared shallow pan. Drizzle remaining olive oil over the the cabbage, and coat the surface with your favorite barbecue rub.

Smoke the cabbage steaks for two to three hours at 275–300 degrees.

Cover the whole pan tightly with foil to finish cooking, and cook until the steaks are tender.