Cut cabbage in half vertically twice, core and slice very thin, separate the pieces.
Cut shallot in thin slices. Take hot pepper, seeds removed, cut in thin slices. (use gloves maybe). Cut carrot in thin, long slices. Can add any other veggies, red pepper, etc.
Combine all veggies in container, large bowl or glass container. Fill to cover wtih white vinegar, add any optional ingredients, any veggies. Add juice from lime. Mix again. Some people add a bit of sugar to counteract the brine.
Store, covered, for a few days and then use. Reuse the brine for the next batch.