Cut the cabbage into quarters, then remove the core. Thinly slice the cabbage, then place it in a large shallow bowl. Sprinkle with the sea salt. Knead the cabbage by hand or with a potato masher for 5 to 10 minutes. After 10 minutes, there will probably be enough liquid released from the cabbage to cover it.
Place ¼ of the cabbage in a quart sized mason jar, then pack it down with a wooden spoon. Repeat with the remaining cabbage, packing down a couple more times. Pour in the brine (the liquid that was released during the kneading process), and add as much water as needed to cover the cabbage. Leave at least an inch of space at the top of the jar. Place a small glass jar (or fermentation weights) on top of the cabbage to keep the cabbage fully submerged.
Cover the jar with butter muslin or a standard jar lid. If you use a lid, make sure to open it every couple days to release the pressure. Place the jar in a bowl in case it leaks. Store it at room temperature (60 to 70 degrees) for at least a week. Taste and see if it’s reached the tanginess you like, and once it has, transfer it to the refrigerator. It will keep for up to 6 months.