Place cabbage pieces in a large bowl. Toss evenly with sea salt. Let sit for 1 to 2 hours, tossing every 30 minutes, until wilted and a brine forms at the bottom.
Rinse the salted cabbage under cold water 2 to 3 times. Taste for saltiness. Squeeze firmly in handfuls to remove excess moisture. Set aside in a clean bowl.
Combine gochugaru, minced garlic, grated ginger, soy sauce, and sugar in a small bowl. Stir into a thick paste. Add green onions and daikon if using, and mix well.
Put on rubber gloves. Add the paste to the squeezed cabbage. Massage thoroughly until every piece is well coated in the red paste.
Pack the kimchi tightly into a clean quart-sized glass jar. Press firmly so brine rises above the cabbage. Leave 1 inch of headspace. Seal loosely.
Leave on counter for 1 to 5 days, away from direct sunlight. Press kimchi down once daily. Taste starting on day 2. Move to fridge when tanginess suits your preference.
Seal the jar and refrigerate. Kimchi keeps for up to 6 months. Flavor deepens over the first 2 to 6 weeks in cold storage.
