Shred the carrots and cabbage finely into a large bowl. You can use the large holes of a box grater or a food processor with a grating attachment.
After resting, use your hands to massage and squeeze the mixture. Keep going until it softens and releases more liquid.
Transfer the mixture to a clean, wide-mouth 1-liter mason jar. Press it down firmly as you add it to help the brine rise and cover the vegetables.