Cut cabbage in quarters and remove core. With a mandolin or food processor fitted with a 2-millimeter slicing blade, slice as thinly as possible. Place in a large bowl with salt and toss to combine.
Transfer to a large glass or ceramic container and tap down by hand so liquid rises to top. Cover with a damp towel touching cabbage and top with a 3-pound weight. Cover again with a layer of plastic wrap and set aside in a warm place for 5 days to ferment. Sauerkraut may be kept in a sealed container in refrigerator as long as 3 weeks.