Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Fill the hole created from coring the cabbage with butter, salt, and pepper. Roll bacon slices and stuff into hole in cabbage. Lay any leftover bacon slices over the top of cabbage. Wrap the whole cabbage in aluminum foil.
Cook cabbage on preheated grill until tender, 45 to 50 minutes. Remove bacon from cabbage and cook on the grill until crisp, 5 to 7 minutes; crumble and sprinkle over cabbage.