Cut the cabbage in half lengthwise, then again into quarters. Remove the core, then cut it crosswise into thin strips.
Place the cabbage in a large bowl and add the salt. With a gloved hand, massage the salt into the cabbage so it's fully distributed.
Cover the cabbage with filtered water and place a plate on top of the vegetable to keep it submerged under the water. Let this sit for an hour
While the cabbage is sitting, prep the carrots, radishes, scallions, ginger, and garlic.
In a small bowl, combine the ginger, garlic, fish sauce (or water, if preferred), red pepper flakes, and sugar.
When the cabbage is ready, drain the water it was in, and rinse it in fresh water. Put it back in the large bowl.
Add the carrots, radishes, scallions, and sauce. Mix well with a gloved hand to fully combine.
Add this to a 32-ounce Mason jar. As you fill the jar, press down on the kimchi with a wooden mallet to enable the liquid to rise above the cabbage mixture to remove any air pockets. Continue filling the jar and pressing out the air until you've added all the cabbage and the jar is almost full. You want to maintain a ½-1-inch space at the top empty. There should be a layer of liquid covering the cabbage and rising above it.
If you have one, place a glass weight (made for this purpose) on top of the kimchi to keep the vegetables below the surface of the liquid. If you don't have a glass weight, use a large piece of cabbage to fold over the mixture to keep it from rising above the water.
Close the lid tightly. If you don't have a lid designed for fermenting, you can use a wide-mouth plastic lid and leave more empty space at the top to account for escaping gas.
Let the jar sit on the counter for 3-14 days. Once it's ready to go (taste it to see if you like it before storing in the fridge), store it in the fridge with a lid for up to a month.