Prepare your vegetables. Peel onion, garlic, and carrots. Remove the outer leaves from your cabbage, core it, and slice. Chop parsley and garlic.
Shred the vegetables. Use a food processor with the grater attachment for ease, or slice cabbage and onion thinly and grate carrots by hand.
Combine everything in a large bowl. Add salt, sugar (if using), chopped parsley, and garlic.
Massage the vegetables with clean hands for about 5 minutes like you were kneading dough, helping them release their liquid. Cover the bowl and let rest for 20 minutes, then massage again until juicy.
Pack the mixture firmly into mason jars, pressing down with your hands or a tool to remove air bubbles.
Pour in extra liquid so the veggies stay submerged. Add brine (made with about 1 tsp salt per cup of filtered water) if needed, and weigh down with fermentation weights or folded outer cabbage leaves.
Cover jars, place them on a dish or tray to catch any liquid, and let them ferment at room temperature. If not using fermentation weights and lids, open jars to press down the veggies and burp any pressure daily. Let the veggies ferment for 5–14 days, depending on your taste and kitchen temperature. Check and taste after a few days.
Once the coleslaw it’s as tangy as you like, store in the fridge. Enjoy as a side dish as is, or stir in a little mayo or ranch dressing for a creamy twist.