Remove the outermost leaves of the cabbage, cut it into quarters and shred cabbage finely (use a mandolin to do this faster and discard the core.
In a large silver bowl, place cabbage, carrots, 2 Tbsp sea salt and 1 Tbsp sugar and scrunch and knead it together really well for the juice to be released from the cabbage (4-5 min). You don't want it to be super juicy, just enough to cover the lettuce when you really pack it down in a jar.
Scrunch it until juices start to come out.
Fill a glass jar with the cabbage mixture and pack it in very tightly so that the juice from the cabbage covers the cabbage completely. You want a jar big enough to be filled only about 2/3 full so it has room to expand.
Make a press over the top of the cabbage by pushing down with a plate (or the lid from a large sour cream container). Top with a small jar of water, a super clean rock or whatever else would make a good weight. Place the lid on the jar but do not tighten. Its a good idea to keep the bottle in the sink or over a dish since there is risk of it overflowing (this is also why we only fill it 2/3 full; it grows!). Let stand at room temp for 4 days or until sour. It will stop fermenting/rising when it's done.
While it sits at room temperature, once each day: poke a few holes through the cabbage with the back of a wooden mixing spoon to release the gas that this process produces and pack the cabbage down tightly.
After 4 days, refrigerate until ready to serve. Can be stored for a few weeks if kept very cold.
To serve, drain the amount of cabbage that you would like to eat by firmly squeezing out the excess juice with your hands. Add in your salad ingredients, mix well and serve.
Notes
*A Note on the Cabbage: buy the ones that are light in color and NOT bright green (the light color indicates that it is a "late" in the year cabbage which works best for this recipe). *The ones at the farmers market in Fall are best. Also, if you are using a soup pot for the fermenting process, don't use aluminum. Start to finish, recipe takes 4 days.