Mix the shredded cabbage and 1-1/2 tablespoons salt together in a non-reactive bowl (glass, stainless steel, or ceramic). Allow to rest for 15 minutes.
Knead the cabbage for 5 minutes by squeezing with clean hands.
Pack the cabbage into a freshly sterilized 1-quart size mason jar. Pack down (try to remove all air bubbles) with a wooden spoon or a wood pounder. Fill the jar up to its shoulder and pour in the brine that kneading produced until the cabbage is covered by about an inch of brine. If there isn't enough brine, make more by mixing together the filtered water and 1/2 teaspoon salt in a glass measuring cup. Pour over the cabbage until the one inch coverage is achieved.
Place a Kraut Source lid (press, spring, moat, and cap) on top of the jar and tighten with the jar's ring. Release the press slowly.
Fill the moat 3/4 of the way full with water.
Place the jar in a dark or semi-dark location (away from direct sunlight) and allow to ferment for at least 5 days (the longer, the tangier the flavor). Refill the moat to 3/4 full as necessary.