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In a separate bowl, mix radish, onion, garlic, ginger, pepper to taste and sugar. If this is your first time trying kimchee, i'd recommend limiting pepper to 3 T. If you're a veteran korean food fan, 5 or 6 will probably be more toward your liking. Use 7 or 8 only if you like really hot food.
Remove cabbage from salt water, reserving brine. Rinse, then chop quarters into 1 inch / 2.5 cm strips (bite size pieces). Discard core.
Mix cabbage and seasoning mixture thoroughly. The easiest way to do this is to put on a pair of sterile rubber gloves and knead away. If you use bare hands, they'll feel sunburned for a day or two. Taste for seasoning. Add more salt and pepper if needed.
Once the mixture is complete, pack it into a glass jar.
Rinse mixing bowl out with brine and pour this over it. Keep adding brine until cabbage pieces are just submerged. Close the jar and stick it on the counter for a couple of days to help it "ripen" (i.e. begins to ferment). Finally, stick it in fridge (tightly-capped, or everything will take on a distinct kimchee aroma).
posted by Julie Vickery