Cut the end off of the cabbage and remove the core. Cut crosswise into 2-inch strips. Place the cabbage in a large, wide bowl and add the salt. Use your hands to massage the salt into the cabbage until it starts to wilt. Cover with purified water and let it stand for at least 2 hours, up to 4 hours.
Meanwhile, combine the garlic, ginger, sugar, fish sauce, and red pepper flakes in the bowl of a food processor and pulse until the mixture is chunky, but well combined (alternatively, if you have a mortar and pestle, now is a good time to use it). Set aside until ready to use.
Drain and rinse the cabbage under cold water and let stand in a colander for 15 minutes. Rinse the bowl you used for salting the cabbage and set aside to use again.
When the cabbage has fully drained, squeeze out any remaining water and add it back to the bowl along with the radish, scallions, and seasoning paste. Wearing gloves (the pepper is hot and the fish sauce is pungent—wear gloves), gently massage the paste into the vegetables until they are well coated. Pack the kimchi into the clean jar, pressing down so any air bubbles escape, leaving about 2 inches of headspace. Secure a paper towel over the jar with a rubber band and let the jar stand at room temperature for 3-5 days (fermentation will happen more slowly at cooler temperatures, more quickly at warmer temps). Taste it after two days, and every day thereafter until it is to your liking. Place a lid on the jar and store in the refrigerator. Kimchi will keep in the refrigerator up to a month.