Cut the cabbage into bite-sized pieces- about 2" wide. Put the cabbage leaves into a large mixing bowl and cover the cabbage in the salt. Make sure all of the leaves are coated in salt.
Allow the salt to sit on the cabbage for 1-2 hours. Once the brining time is up, rinse thoroughly under cold, running water.
Strain the leaves well, then and squeeze them as dry as possible. Lay the leaves onto a clean kitchen towel, then pat the leaves as dry as you can with another towel, or with a couple of paper towels.
Combine the sugar, sesame oil, fish sauce, anchovy paste, gochugaru, and 1 tablespoon of the hot water in a large bowl (the same bowl you used for salting the cabbage is great). Make a thick paste, the consistency of tomato paste. Add more water if needed.
Add the green onions, garlic, ginger, radish to the paste.
Use your hands to add the cabbage to the paste in the bowl and massage the pepper paste into the leaves thoroughly. You want the leaves to be fully covered.
Pack the cabbage into a glass jar, or into a traditional ceramic onggi.
Cover the jar and allow the kimchi to sit at room temperature for 1-3 days. Keep an eye on the kimchi as you may need to "burp" the jar once a day to release the pressure that has built up during the fermentation process. If the lid has started to bulge, twist the lid open to vent it a little, then recover.
After 24 hours, the kimchi may be transferred to the refrigerator to slow down the fermentation process considerably. If prefer to have a tangy, really fermented kimchi, leave it at room temperature for the full 3 days. If you're a kimchi novice, I recommend the 1 day ferment.
After you've transferred the kimchi to the refrigerator, it's best if it's consumed within 2 weeks.