Remove the outer leaves from the red cabbage. Quarter it and cut out the tough core. Shred into fine strips using a mandoline, food processor, or sharp knife. Add to a large bowl.
Heat 2 tbsp of the oil in a skillet over medium heat. Add the onions and cook, stirring occasionally, until softened and lightly browned, about 8 to 10 minutes.
Add the remaining oil, apple cider vinegar, balsamic vinegar, sugar, and salt to the pan. Stir and bring to a rolling boil.
Immediately pour the hot dressing over the shredded cabbage. Toss well to coat everything evenly.
Leave to cool to room temperature, then season with freshly ground black pepper and scatter over the parsley if using.
Rest for at least 2 hours before serving, or ideally overnight. Taste and adjust seasoning before serving.
