Cabbage is one of the few vegetables I routinely add extra aromatics to when pickling.
Prepare the brine as above. Fill your jar with finely sliced cabbage. Push 2 or 3 peeled garlic cloves and 2 bay leaves into the center of the cabbage. Fill the jar with brine, cover it with plastic wrap, and press the cabbage down with an appropriate glass or other weight. Refill the remainder of the jar and cover loosely. (Alternatively, press the plastic wrap down well below the rim of the jar and, holding it down, fill the jar so that the weight of the brine and the plastic wrap barrier hold the cabbage down, then cover loosely.)
Brine at cool room temperature for 5 to 7 days. Serve hot or cold, or refrigerate in a 3 percent brine as noted above.