Wash and gently scrub the outside of a head of cabbage. Remove any blemished outer leaves.
Trim off two to three large outer leaves and set aside. These leaves will be used in place of fermenting weights if you do not have them.
Cut the head of cabbage in quarters. Trim off the core from each quarter piece. Using a very sharp knife cut the cabbage into very thin shredded ribbons.
Transfer the shredded cabbage to a large bowl. Add the pickling salt and caraway seed if you are using it.
Using clean hands toss the cabbage with the salt. As you toss to cover the cabbage with salt squeeze the cabbage to massage the salt in. Do this for about 3 minutes until the salt is evenly distributed.
If you have a wooden vegetable tamper pound the cabbage until the cabbage is compressed, squeezing out more liquid. If you don't have a vegetable tampering tool you can place a heavy saucer on top of the cabbage and weight it down so it will compress the cabbage and help it release moisture for the brine.
Place a lint free towel over the top of the bowl and allow the cabbage to release moisture to create the brine. This process can take a couple of hours up to 48 hours.
Transfer the cabbage and all of the liquid to one or more wide mouth canning jars. Use a wooden sauerkraut pounder to compress the cabbage in the jar. Only fill the jar to the shoulder of the jar to leave space for the weight.
Place the fermenting weight into the jar if you have one. If you don't you will need to use the whole pieces of cabbage leaves you saved when you trimmed the cabbage earlier.
Place a silicone fermentation airlock lid on top of the jar. If you don't have one cover the jar with cheesecloth or a coffee filter.
Screw a canning lid band over the the airlock lid. Place the jar out of direct sunlight on the kitchen counter.
Place the jar in a safe spot on the kitchen counter that is not in direct sunlight. Allow the sauerkraut to ferment for about 1 month. The airlock system will allow gasses to escape naturally as the cabbage ferments. Check the brine level weekly. (see recipe notes)
Occasionally, if needed manually release the gasses by squeezing the nob on the silicone top.
After 2 weeks you can open the jar and taste a piece of the sauerkraut. It should be firm and crunchy with a pleasant sauerkraut odor and flavor.
Once the sauerkraut has reached the perfect fermented flavor you like remove the airlock lid, the fermentation weight and cover the jar with a lid and refrigerate.