1. Cut the cabbage into quarters and remove the core. Cut each quarter into 2-inch wide strips.
2. In a large bowl, sprinkle salt over the cabbage and toss to combine. Let it sit for 1-2 hours, tossing every 30 minutes.
3. Rinse the cabbage under cold water 3 times to remove excess salt. Drain well.
4. In a separate bowl, combine garlic, ginger, sugar, and fish sauce to make a paste.
5. Add the radish, green onions, and gochugaru to the paste. Mix well.
6. Wearing gloves, gently work the paste into the cabbage until it is thoroughly coated.
7. Pack the kimchi into a glass jar, pressing down to remove air pockets. Leave some space at the top for expansion.
8. Let the kimchi ferment at room temperature for 1-2 days, then refrigerate.