1. Cut the cabbage into quarters and remove the core. Cut each quarter into 2-inch wide strips.
2. Place the cabbage in a large bowl and sprinkle with salt. Toss to combine and let sit for 1-2 hours, tossing occasionally.
3. Rinse the cabbage under cold water to remove excess salt. Drain well and set aside.
4. In a separate bowl, combine the gochugaru, garlic, ginger, fish sauce, green onions, and carrot. Mix well to form a paste.
5. Wearing gloves, add the paste to the cabbage and mix thoroughly, ensuring all the cabbage pieces are coated.
6. Pack the kimchi tightly into a jar, pressing down to remove air bubbles. Leave some space at the top for expansion.
7. Let the jar sit at room temperature for 1-2 days to ferment. Once fermented, store in the refrigerator.