Cut each head of cabbage in half and then cut the core out. Then cut the two pieces into smaller sections to ease the slicing.
Thinly slice the cabbage to about ⅛ inch thick, the use of a mandolin would be perfect for uniform slices.
Place the cabbage in a large mixing bowl and add ¼ of the salt needed. Use your hands to mix the salt into the cabbage. Then add a ¼ more of the salt and mix in, repeat this 2 more times until all of the salt is mixed in. Set the bowl aside for 30 minutes.
After 30 minute, the cabbage will have wilted and reduced in volume and liquid accumulated in the bowl, perfectly normal.
Now sprinkle in the caraway seeds, mustard seeds, and garlic. Use your hands and mix together well. Once again, set aside for 30 minutes.
Now transfer the cabbage and liquid into the jar and allow at least 1 inch of space at the top of the jar. Making sure the cabbage is below the level of the liquid.
Cover the jar with cheesecloth and secure with a rubber band or string. Write down the date you do this. Leave the jar on your counter top, (away from any cats, cats like to push things off counters).
Check the jar each day to make sure the cabbage is covered with the liquid. If it is not, remove the cheesecloth and tamp down the cabbage. If additional brine is needed, mix 1 cup of water with 1 teaspoon of salt and add that as needed.
Check the kraut each day for 7 days, adjusting as needed.
On the 7th day, sample the kraut, you should have good kraut now, use in other recipes as directed. If the taste is good, you can ferment longer for a stronger flavor.
You should now have ½ gallon of kraut.