Place cabbage in a large bowl and sprinkle with salt. Toss to coat the cabbage with salt. Cover with water and toss again. Let sit for at least 10 minutes or up to 2 hours. Drain and rinse the cabbage. Dry thoroughly. Place in a dry bowl.
In a small bowl, combine gochujang, vinegar, fish sauce, garlic, and ginger. Add to the cabbage with the carrots and green onions. Toss well.
Can be eaten right away or stored, covered, in the refrigerator for up to 2 weeks.