Cut the cabbage into quarters and then chop into bite-sized pieces. Combine napa cabbage, daikon, and carrots in a large glass or any non-reactive bowl.
Dissolve the salt in the water and pour in the bowl. Gently stir and press down to submerge the vegetables. Use a plate with a weight on top to hold down the vegetables and soak in salted water for at least 2-3 hours or overnight.
Drain the vegetables, reserving the brine. Add garlic, ginger, scallions, and gochugaru to the brined vegetables and massage everything together until well combined.
Pack the mixture into jars, pressing down to release the brine so it covers the vegetables. Add reserved brine to fully cover the vegetables, if necessary. Leave about an inch of space at the top.
Loosely cover the jar with a lid and let it ferment at room temperature for 4–7 days, depending on your taste preference. Once a day, gently press down the vegetables in the jars to allow gas to escape.
Once kimchi is fermented to your liking, store it in the refrigerator.