Cut the cabbage lengthwise into quarters. (I leave the core in–it has crunchy appeal once fermented.) Cut each quarter crosswise into 1 to 2-inch-wide strips. Place the cabbage in a large bowl, and sprinkle it with the salt. Wearing gloves, if desired, massage the salt into the cabbage until it starts to soften a bit (1 to 2 minutes) and then add water (about 2 quarts, depending on dimensions of the bowl) to cover the cabbage. Put a plate over top, and use a jar or can to weigh the plate down. Let the mixture sit at room temperature for 1 to 2 hours.
Once the cabbage has soaked, rinse it briefly under cold water and let drain in a colander for about 10 minutes. Rinse and dry the bowl that you used for soaking, and set it aside.
For the spice mixture: Using the back of a fork in a small, wide bowl, mash the garlic, ginger, and sugar together until a fairly smooth paste forms. Mix in the fish sauce and the Korean red pepper powder (gochugaru). For a spice level similar to a medium salsa, I recommend 2 1/2 to 3 tablespoons of the powder; adjust up or down according to taste, staying within the 1 to 5 tablespoon range.
Next, gently squeeze or shake any excess water from the cabbage, and return it to the bowl along with the radish, carrots, scallions, and seasoning paste. Using your hands, gently work the paste into the vegetables until they are thoroughly coated. (Gloves are optional but recommended to protect your hands from stains–and the spice sometimes irritates my skin.)
Pack the kimchi into a large jar or or crock. Press down on the kimchi until any liquid rises to cover the vegetables. More liquid (brine) will develop as the kimchi ripens. When using a container with a wider opening, I use a plate with a jar or can on top to weight down the kimchi. Cover with a lid.
Now you just have to wait. Allow the kimchi to stand at room temperature for 3 to 5 days. Bubbles may form and brine may seep out of the lid if using a jar that’s close to full. To catch any overflow, place a bowl or plate under the jar.
Check the kimchi once each day, pressing down on the vegetables with the back of a spoon to allow the brine to rise up and cover them. After a few days, taste some of the kimchi and when it tastes ripe enough for your liking, transfer to the refrigerator. At this point, I usually transfer to several pint-size jars for convenient storage. (Just make sure to use a canning or plastic lid, which are non-reactive.) You may eat the kimchi right away, but the flavor will continue to develop. It’s best to be patient and wait another week–or two if you can. The refrigerator life of kimchi is at least month, but likely much longer.