Remove the tough outer leaves from the cabbage. Cut each head into quarters and remove the tough core. Thinly slice the cabbage into ribbons. The thinner the cabbage, the more readily it will ferment.

Place the sliced cabbage in a large mixing bowl. Sprinkle with the sea salt and add the shredded carrots. Toss everything together, then allow the mixture to rest for about 5 minutes.

Using clean hands or a fermenting stomper, work the salt into the cabbage and carrots for about 5 minutes, or until the vegetables soften and begin releasing their juices. Continue pressing and stomping as needed to help draw out enough liquid to create a natural brine.

Add the cabbage and carrot mixture to your clean fermentation crock a little at a time, packing it firmly with your fermenting stomper. After adding a layer of the cabbage mixture, scatter in some cranberries. Continue alternating layers of cabbage and cranberries until all the vegetables and berries have been added.

Pour any remaining juice from the mixing bowl into the crock. Press the mixture down firmly, ensuring the vegetables are submerged beneath the brine. If there isn't enough liquid to cover them, add a little prepared salt brine at the appropriate concentration for your fermentation method.

Place a fermentation weight over the vegetables to keep them beneath the brine, then seal the crock according to the manufacturer's instructions.

Leave the crock to ferment at a suitable room temperature for at least 6 weeks before tasting. For a deeper, more pronounced sourness, allow it to continue fermenting longer, checking periodically until it reaches your preferred flavor.

Once the sauerkraut has developed the flavor you enjoy, transfer it to clean jars and refrigerate. Keep the vegetables submerged in their brine during storage.