Cut, core, and shred the cabbage finely using a Mandolin slicer or put it through the slicing blade on the food processor. Transfer shredded cabbage to a large glass bowl.
In a small saucepan, add the filtered water, apple cider vinegar, and sugar and bring to a gentle boil over medium low heat. Once the sugar has dissolved, turn the heat off. Then stir in the minced garlic, kosher salt, black pepper, dried red chili pepper, dried basil, dried dill weed, and the essential oils.
Pour the pickling liquid over the shredded cabbage allowing the liquid to cover the cabbage. Using a 32 ounce glass Mason jar, transfer the pickled cabbage mixture and cover with the lid. Let the jar sit at room temperature on the kitchen counter for at least 4-5 hours before placing it in the refrigerator.
The pickled cabbage can be kept in the refrigerator for one month.