Cut the knot from the bottom of the cabbage and remove the core.
Heat 1 tablespoon butter in a skillet over medium heat; cook and stir onion until softened, about 10 minutes.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels, reserving bacon drippings. Chop bacon into small pieces. Mix onion, bacon, and barbeque sauce together in a bowl.
Fill the hole in the cabbage with onion-bacon mixture and place pieces of butter into the core to fill completely. Drape 2 bacon strips over filling and hold in place with toothpicks.
Preheat an outdoor grill for medium heat and lightly oil the grate. Make a ring out of aluminum foil and place on grill.
Place cabbage on the foil ring and cook, basting with bacon drippings, until a fork can easily puncture the cabbage, 15 to 30 minutes.