Rinse cabbage and remove the outer leaves. Slice thinly, with either a knife or the shredding attachment of a food processor. You may slice it thin or thick, but the key is making it uniform in size.
Place shredded cabbage in a large metal or glass bowl. Sprinkle with salt. Massage salt into the cabbage; it will start to release water. Continue massaging until you have quite a bit of water and cabbage starts to soften. This might take a few minutes, and it does require some arm and hand muscles!
Using a large glass jar, press cabbage into the container. Do this slowly, with just a cup or two at a time so you can really press down. You want to compact the cabbage as much as possible to eliminate air bubbles and release more water.
Once all of the cabbage is in the jar, place something heavy on top (like another jar filled with water) to weigh it down. Press down hard until water covers the cabbage. Ideally, you want at least 1 inch of water on top.
Cover jar with a cloth and secure it with a rubber band.
Place the jars on a plate or rimmed baking pan and allow jars to sit on the counter or in a cupboard, for a range of 2-6 weeks. The cabbage will start to bubble and may leak over the edges, this is normal.
Check the cabbage every few days, push any floating cabbage back under the brine. After a week taste the cabbage. It should be tangy. If any of the cabbage has turned dark and begun rotting, you can scoop that out and make sure the remaining is under then brine. If some mold appears on the top, it is normal, just remove an inch of the cabbage and eat what is underneath.
Once it reaches the tanginess you like, remove cloth and top with a lid and refrigerate. Enjoy small servings.