**Prepare the bok choi:** Separate the bok choi leaves from the stems. Cut the stems into 1-inch pieces and soak both leaves and stems in a large bowl of cold water with the coarse sea salt for 2 hours. This process helps remove bitterness and softens the vegetables.
**Make the kimchi paste:** In a separate bowl, combine the gochugaru, fish sauce, garlic, ginger, green onions, carrots, and daikon radish. Mix well to form a thick paste.
**Drain and rinse the bok choi:** After 2 hours, drain the bok choi and rinse thoroughly with cold water. Pat dry with paper towels.
**Coat the bok choi:** Spread the kimchi paste evenly over the bok choi leaves and stems. Ensure that all surfaces are well-coated.
**Ferment:** Place the coated bok choi in a clean glass jar or airtight container. Press down firmly to remove any air pockets. Cover the jar loosely with a lid and let it ferment at room temperature for 3-5 days.
**Refrigerate:** Once the kimchi has fermented to your desired level of sourness, transfer it to the refrigerator. It will continue to ferment slowly, developing more complex flavors over time.