Cut the cabbage into bite-size pieces. Toss with the salt in a large bowl and let it sit 1 hour, tossing every 20 minutes, until the pieces bend without snapping and have released noticeable liquid.
Meanwhile, simmer the dried shiitake and kelp in the water for 15 minutes. Remove the kelp and set the stock aside. Finely chop the softened shiitake caps — don't discard them, they're doing most of the savory work here.
Rinse the salted cabbage twice in cold water and drain well in a colander, pressing gently.
Whisk the rice flour into 1 cup / 250 ml of the mushroom-kelp stock and simmer 3 to 4 minutes, stirring, until it thickens into a thin, glossy porridge. Cool it before using.
Stir the cooled porridge together with the chopped shiitake, gochugaru, soy sauce, sugar, grated pear, onion, garlic, and ginger into a thick, spreadable paste.
Fold the radish and scallions into the paste.
Add the drained cabbage and toss by hand, gloved if you'd rather not smell like chili, until every piece is coated.
Pack tightly into a clean container, pressing so the released liquid rises above the solids. Leave at room temperature 1 to 2 days, until small bubbles appear at the edges, then refrigerate.