Wash jars in warm, soapy water. Place the washed jars in a deep pot or canner. Fill the jars up to the top and the canner up to the same level as the jars with water. Cover the canner and bring water to a simmer (with small bubbles).
Wash metal bands and silicone fermentation lids with warm soapy water. Drop the metal bands (but not the silicone fermentation lids) into the canner together with the jars. When ready to use, take them out from the canner with a pair of tongs. Dry them with a clean towel. If you are using plastic bands, wash them with warm soapy water but do not drop into canner.
Remove and discard any blemish leaves from the red cabbage. Peel off one whole leaf from each red cabbage, rinse, and cut two circles (the diameter of 1 quart Mason jar) out of reserved cabbage leaves. Set aside.
Cut cabbage into quarters and then cut off the cores from each cabbage quarter. Rinse and drain cabbage quarters thoroughly.
Place one wedge of cabbage on your cutting board with cut side down. Slice crosswise as thinly as you can. Transfer sliced cabbage to a large bowl and sprinkle some of the salt over the sliced cabbage. Keep slicing cabbage, adding it to the bowl, and sprinkling salt in layers until all cabbage quarters are sliced.
Add julienned apple and sliced onion. Sprinkle caraway seeds over the top.
Toss, squeeze, and massage shredded cabbage well to incorporate julienned apple, sliced onion, salt, and caraway seeds evenly. This will take some work, about 4 to 5 minutes, and you should see some juices/brine being released. Use a wooden tamper/pounder to pound and mix the cabbage for another 4 to 5 minutes until cabbage is wilted and juicy.
Pack cabbage into prepared jars with a couple of handfuls of cabbage at a time. Use wooden tamper/pounder to pack it down firmly. Continue adding and packing down the cabbage until the jar is filled to just below the shoulder. The brine should rise up to the top. Do not overfill jar.
Place a cut-out cabbage circle on the surface of shredded cabbage to prevent little bits from floating up. Place a weight on the top to keep the shredded cabbage submerged in the brine.
Wipe the rim of the jar with a paper towel, place a silicone fermentation lid on the rim, and secure with a Mason jar band. Place jars on a tray just in case the brine overflows the jar. Transfer to a cool, dark place to ferment with preferably an ambient temperature between 60⁰F and 70⁰F / 15⁰C and 21⁰C.
Fermentation should begin within 2 to 3 days. As it proceeds, you will notice these changes:a. The cabbage swells up so that the brine almost touches the lid.b. Pockets of gas appear in the cabbage.c. The color of the red cabbage changes from purple to magenta-fuchsia.d. Bubbles appear on the surface of the brine.e. A sulfurous aroma emitting from the jar.
Taste Test
After 5 days, open the jar. If there is any scum at the top of the jar above the cabbage circle, scoop it up and discard. If the fermented cabbage is completely under the brine, it will be good. Remove the weight and cut-out cabbage circle, and have a taste. The cabbage should be a magenta-fuchsia color by now. The salty flavor should have diminished and be replaced with a bright and tangy flavor of the lactic acid.
I left mine to ferment for 5 days which I felt was just right for the conditions in my house. The cabbage was soft but still crunchy and it has a pleasant bright and tangy flavor, but not too tangy.
If you are satisfied with the taste of the cabbage, wipe off any scum with a clean towel and reseal the jar with a plastic lid. Store in the refrigerator for 4 to6 months.