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Wash the heads of cabbage. Remove any sketchy outer leaves, then quarter each head and cut out the woody core. Shred each quartered head as thinly as you can (or use the Cuisinart with 2mm blade), aiming for long, thin, spaghetti-like strands.
Put the shredded cabbage and salt into the largest bowl you have — a clean dishpan works. With clean hands, dig in and massage the cabbage so that the salt is evenly distributed and begins to draw out moisture. It helps to let the bowlful sit on the counter for an hour or so, massaging now and then.
Put the cabbage and all juice into a crock or food-grade bucket. Really squeeze it down to eliminate any trapped air bubbles. Use your fists or a flat-bottomed potato masher to get it as tightly packed as you can.
Ensure that the cabbage remains below the surface of the liquid. (See note on liquid below.) This is an anaerobic fermentation: If air reaches the cabbage, the whole batch could be ruined. Put it somewhere out of the way — the basement, for example. Length of fermentation is a matter of personal taste. Four or five weeks is good; it keeps getting stronger.
When it has fermented to your taste, pack the finished sauerkraut and its juice tightly into quart mason jars or other storage containers and stash it in the fridge. It will keep for up to a year. You can do the home-canning hot-water bath routine, but you will sacrifice taste and crunch and end up with the insipid canned stuff you can buy at most grocery stores.
Considerations
Liquid. Some sources suggest leaving the cabbage-salt mixture (step two above) on the kitchen counter for half a day so the salt can continue to draw out moisture. If you are skittish about that, add a cup or two of saltwater (1 teaspoon of salt per cup of water; use filtered or bottled water rather than tap for the same reason you use kosher salt). If your cabbage was middle-aged or older, you may need to add volume to its natural juices.
Salt. Be absolutely certain to use pure salt (kosher or canning salt). Table salt with anti-caking additives will not produce the fine fermented product you’re looking for. Although these measurements allow for leeway, they are a good starting point. Too much or too little salt can adversely affect the fermentation process. Figure three tablespoons per five pounds of trimmed, shredded cabbage. The recipe can be doubled, tripled, etc., but it’s easier to work in batches.
Fermentation vessel. The best is a two- or three-gallon crock. It’s echt, heavy, and helps maintain a constant temperature. The forebears made kraut in 10-gallon batches or more to last the winter. Any large food-grade container will do.
Weight. Keeping the cabbage under the surface of the liquid is essential. Most sources suggest placing a plate or pie pan slightly narrower than the vessel on top of the cabbage, then adding a weight (e.g., a large jar filled with water or a large stone that has been scrubbed and boiled). If you use that system, check the vessel every two or three days. If there is scum or foam, remove it (paper towels work), then put in a new clean plate — but keep the cabbage submerged. Many crock manufacturers also sell ceramic weights to fit crocks of various sizes. Another approach is to use a large food-grade plastic bag filled with a quart or two of saltwater (in case of puncture; see note on liquid, above). Setting that bag atop the cabbage will provide an edge-to-edge seal. Just remove any flecks of cabbage that may have made it to the surface. You don’t have to check it as often, unless you’re curious.
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