Remove the core from the head of cabbage. You can do this by cutting around the core with a sharp knife, then slicing the core out.
In a bowl, mix the softened butter, smoked paprika, garlic powder and cooked bacon pieces together. Mix all of these ingredients until they are incorporated well together.
Stuff the butter mixture into the hollowed out section of the cabbage where the core was. Then place the cabbage in the center of a large square of heavy duty aluminum foil, core side up. Wrap the foil around the cabbage, creating a bowl of sorts, allowing the core to remain exposed. Pour the chicken broth over the cabbage around the core area.
Place the cabbage, still core side up, on the grill. You want to use indirect heat for about an hour. After an hour, wrap the foil the rest of the way around the cabbage, securing it tightly. Then grill it for another hour and a half.
Once the cabbage is cooked, place it in a large bowl. Start by cutting it into quarters and continue cutting until you have your desired size of pieces. Mix it up to incorporate the bacon and juices throughout. If there are juices left in the bottom of the foil, pour them over top and mix again.