Cut out cores of the green cabbage and roughly chop into 1-inch pieces. Separate the layers into a large bowl. Add salt and water. With your hands, mix and separate the cabbage layers for about 1 minute. Leave on the side for 15 minutes, mixing every 5 minutes.
White waiting for the salt to work its magic on the green cabbage, slice the carrots and chop the green onions and garlic.
Rinse the green cabbage with running water twice. Place in a colander to drain for 5 minutes.
In a large mixing bowl, add the green cabbage, carrots, green onions, garlic, Korean red chili pepper flakes, raw sugar, and fish sauce. Mix with your hands until everything is fully incorporated. Transfer the kimchee to a large container and push down to force the air out. You want as little air as possible throughout the kimchee.
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Notes
You can eat this right away, but it's best to let it sit in the fridge for at least one day to allow the flavors to soak in.
Use clean utensils to take out the kimchee from the container. Dirty utensils will make the kimchee spoil faster (especially oily utensils).
The cabbage cores can be thinly sliced and added to soups as they will soften up nicely and add good flavor.