In large bowl, combine brine ingredients. Stir to dissolve.
Remove coarse outer cabbage leaves; rinse a few of the unblemished leaves and set aside. Rinse cabbages in cold water, trim off stalk ends, and cut each in half. Submerge cabbage halves and reserved outer leaves in brine. Use a plate as weight to keep cabbages submerged. Set aside, at room temperature, for 6 to 8 hours.
Drain cabbage for 15 minutes, reserving 1 to 2 cups of brining liquid. Set separated outer leaves aside. Meanwhile, combine chili pepper flakes (gochugaru), daikon, carrot, scallions, garlic, and ginger in a large bowl; blend thoroughly.
Chop brined cabbage into bite-sized pieces; add to the bowl. Massage mixture thoroughly. Taste, adding more salt if desired.
Transfer vegetables, a few handfuls at a time, into jars, pressing down with your hands. Add reserved brine to submerge vegetables, leaving about 2 to 3 inches of space per jar. Cover with brined leaves.
Set jars aside on baking sheet to ferment, and be sure to place them out of direct sunlight. Check daily to ensure vegetables are submerged, and skim off any foam. Or screw on lid and refrigerate for a milder-tasting kimchi. Allow 7 to 14 days to ferment.
After 1 week, taste. Store in the refrigerator. Kimchi will keep, refrigerated, up to 9 months.