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Cut the napa cabbage in half longways, then in half again longways. Cut the core out of the four quarters. Cut the cabbage into squares (about 2-3 inches square), pop it in a bowl with the carrots. Sprinkle with the 1/2 cup kosher salt, massage so everything is coated in salt and starting to soften and wilt. Fill with cold, chlorine free water to cover it well and let it soak for at least 1 1/2 hours.
Pour the cabbage and carrots and liquid into a strainer. Let the brine drain away.
Lob off the white bits of the green onions and put them in a food processor with the garlic cloves, ginger, miso paste, and korean pepper powder. Zap it on high 'til it's smooth-ish. Add in the fish sauce and a couple of slops of pear juice and zap it more until it's about pancake batter consistency... maybe a bit thinner.
Put the brined cabbabe/carrots in a big, anti-reactive (glass, enamel, or stainless steel) bowl. Rough chop the green parts of the onions and add those to the cabbage/carrots. Pour the chili paste combo over the cabbage and wear gloves to massage it all over the cabbage/carrots green onions so everything is completely covered.
Pack super tight in canning jars. CRAM it in there. Add a two-piece lid, but just set the ring in place to hold the lid down without screwing it in place. Place it on a rimmed baking dish to catch any spill-over. Let it sit at room temperature for up to 72 hours, until it is bubbly and fragrant. Once every day, insert a clean chopstick or butterknife to release air bubbles. If needed, pour in some additional brine to keep all the vegetables submerged.
Store on a rimmed sheet in the refrigerator for up to six months, being sure that the vegetables are submerged the whole time. The older it gets, the stronger it will become.