Shred cabbage finely into a large bowl. Sprinkle with 1 tablespoon salt and squeeze/massage the cabbage with your hands for 10–15 minutes to soften the cabbage and extract the water (keeping water in the bowl). Add the other tablespoon of salt midway through the massage.
Pack the cabbage and its liquid into 4 wide-mouthed pint Mason jars. Pack the cabbage down so that the liquid is covering the cabbage. Leaving the jars open, place a weight on the cabbage so that it is completely submerged under the liquid (we used small juice glasses filled halfway with water).
Store the kraut for 3 weeks at room temperature, in a cool, dry, dark place (can ferment longer for stronger flavor). Monitor the jars regularly, adding more water if necessary to keep the cabbage covered.
After 3 weeks, remove the weights and any mold (called the “mother”) that may have formed on top. Pour off some of the liquid, seal jars and refrigerate. Will keep refrigerated for 2–3 months.