Mince and grate ingredients. Place all ingredients in a bowl. Massage and squeeze to release the juices.
Place mixed ingredients into a 2–quart-sized wide mouth mason jar and cover with outer leaves of the cabbage to weigh it down.
Add filtered water. The top of the vegetables should be covered, with liquid 1-inch below the top of the jar.
Cover tightly, opening at least once daily to release the pressure and ensure the cabbage mixture remains under the liquid without overflowing. Keep away from sunlight for at least 10 to 14 days before transferring to cold storage.
Fermentation time varies depending on preference, temperature, salinity, and freshness of ingredients. If you’re in a hurry you can ferment for as little as 5 days, although the cabbage will be crunchy. Traditional sauerkraut is typically fermented for several weeks.