Cut the napa cabbage into quarters and remove the core.
In a large bowl, dissolve salt in water and soak the cabbage for 2 hours.
Rinse the cabbage under cold water to remove excess salt and drain well.
In a separate bowl, mix ginger, garlic, sugar, fish sauce, and gochugaru to form a paste.
Add green onions, carrot, and radish to the paste, mixing thoroughly.
Wearing gloves, coat the cabbage pieces with the spice mixture.
Pack the coated cabbage tightly into a clean jar, pressing down to remove air pockets.
Leave about an inch of space at the top of the jar.
Cover the jar loosely with a lid or cloth to allow fermentation gases to escape.
Let it ferment at room temperature for 1 to 5 days, tasting daily until it reaches your preferred tanginess.