To prepare the cabbage: Cut the cabbage lengthwise into quarters, then cut each quarter into 5 cm pieces. Place them in a large bowl and sprinkle with coarse salt. Mix well to coat the cabbage. Let it sit for about 1 hour, turning the cabbage occasionally. This will allow the cabbage to release some of its water.

Rinse the cabbage: After an hour, rinse the cabbage thoroughly in cold water to remove excess salt. Drain well.

To prepare the spiced paste: In a bowl, mix the minced garlic, grated ginger, green onions, julienned carrot, sugar, chili, and fish sauce if using. You should obtain a thick, smooth paste.

Season the cabbage: Mix the drained cabbage with the spiced paste. Wear gloves if possible to thoroughly rub the paste onto each cabbage leaf.

Fermentation: Place the seasoned cabbage in an airtight jar, pressing firmly to remove any air bubbles. Let it ferment at room temperature for 1 to 5 days, depending on your kitchen temperature. It's best not to open the jar to avoid bacterial contamination. After 3 days, you can taste it, and if the fermentation is to your liking, store the kimchi in the refrigerator.