Cut the napa cabbage into quarters and remove the core. Cut the cabbage into bite-sized pieces.
In a large bowl, mix the cabbage with the kosher salt until it is well coated. Let the cabbage sit for 2-3 hours, stirring occasionally.
Rinse the cabbage in cold water to remove the salt. Drain the cabbage in a fine mesh strainer and let it sit for 30 minutes to release excess moisture.
In a mixing bowl, combine the gochugaru, fish sauce, sugar, rice vinegar, chopped onion, shredded carrot, minced garlic, and grated ginger. Mix everything together to form a paste.
Add the drained cabbage to the paste and mix everything together until the cabbage is well coated.
Transfer the kimchi to a large airtight container. Press the kimchi down to remove any air pockets, and then seal the container.
Let the kimchi ferment at room temperature for 3-5 days, until it is tangy and slightly sour. Open the container once a day to release any built-up gas.
Once the kimchi is fermented to your liking, transfer it to the refrigerator. The kimchi will continue to ferment in the refrigerator, but at a much slower rate.