Finely (or chunky if preferred) slice, grate, or chop cabbage and beets (for tips on less messy prep, click here).
Place beets and cabbage in a large bowl and sprinkle 1 tbsp salt over mixture. Let sit for 15-20 minutes.
Massage (mash, press, or crush) mixture for about 10 minutes to get the juices flowing! Massaging mixture should create a lovely beet cabbage juice at the bottom of the bowl.
Mix in garlic cloves, fresh ginger, caraway seeds, and dill.
Leave ingredients in bowl on counter for about an hour until cabbage has wilted a bit and released more salty juice (water).
Once cabbage/beet mixture is watery, pack mixture and juice into clean mason jars. Firmly pack down mixture (a wooden spoon works well). You want to eliminate as many air bubbles as possible. Keep packing until the jar is almost full (leave at least 1-2 inches at the top for expansion).
Liquid should lightly cover mixture. If there is not enough liquid to cover the cabbage, mix 1 salt tbsp with 4 cups water, and add brine to bring the water level enough to cover cabbage.
If cabbage floats, use a glass weight or piece of cabbage core to hold it down.
Affix jar lids and set aside in room temperature (no direct sunlight) for about ONE WEEK.
Placing jars on a dish or tray helps eliminate any messy leaking or spilling over. Additionally, “burping” the jar every day or so releases pent-up gasses. To do this, remove the lid (preferably over the sink), release the gasses, and also press down any floating pieces. You don’t want to introduce any non-clean bacteria to your mixture, so make sure any utensils or fingers used are clean and sterile!
Taste your kraut after one week. If it has reached the right amount of flavor and tang, store jars in the refrigerator. If you wish to ferment your kraut further, leave at room temperature for a few more days or another week.