1. Cut the cabbage in half lengthwise, then crosswise into 2-inch pieces. After discarding the root ends, place the chopped cabbage in a large bowl. After sprinkling the cabbage with salt, toss the cabbage to thoroughly mix. Add enough cold water to submerge the cabbage (about 12 cups), and then cover the bowl with plastic wrap let it sit at room temperature for between 12 – 24 hours.
2. After 12 – 24 hours has passed, drain the cabbage in a colander, rinsing it with cold water. Gently squeeze out the excess liquid and transfer to a medium bowl, and set the cabbage aside.
3. Place the remaining ingredients (radish, scallions, red pepper, fish sauce, ginger, garlic, minced shrimp, and sugar) in a bowl together and stir to combine the mixture completely.
4. Add the cabbage in with the rest of the ingredients. Toss everything together until the mixture is evenly distributed throughout the cabbage and everything is combined.
5. Pack the mixture tightly into a clean 2-quart glass jar with a tight fitting lid and seal the jar.
6. Let the mixture rest in a cool, dark place for 24 hours, and don’t be alarmed if it bubbles (that’s our friend Lactobacillus talking). Open the jar to let the gases escape, then reseal and refrigerate at least 48 hours before eating, but for ideal results let it ferment for a week. This will make for a much more robust and flavorful kimchi! The kimchi will keep for one month if refrigerated.