Cut cabbage into slices about 1 1/2" wide.
Layer the cabbage with salt into a large bowl. Cover with water and let it sit overnight. The next morning it will be tender.
In the morning, wash it 2-3 times to get the salt off and place it back in a large mixing bowl.
Peel the radish and cut into matchstick size pieces. Add to the cabbage.
Slice the cooking onion in half and then slice each half thinly. Add to the cabbage.
Trim the scallions and cut into 1" chunks. Mince in food processor until finely chopped. Add to the cabbage.
Add the ginger, red pepper powder, fish sauce, garlic and shrimp to the cabbage. Stir gently with large spoon or hands until combined.
Stuff the kimchi into a 1 gallon glass jar (lid should be plastic, not metal) and use a rock to hold the fermenting cabbage down. Leave the jar on the counter for 1-2 days. The mixture may foam as it ferments. This is normal. If the jar is very full, try placing it in a bowl to catch any drips.
After 1-2 days, open the lid and let any accumulated gasses escape. Then recover the jar with the lid, wash outside of jar if needed and place in the refrigerator.
The Kimchi needs to ripen for about 5-6 more days. You can eat it while it is ripening but it will be best after this time.
Usually Kimchi stays good in the refrigerator for about a month. After that Americans usually toss it and Koreans boil it into soup.