Dissolve 1/2 cup coarse salt in a large bowl of water. Submerge cabbage in the salted water and let soak, 12 to 24 hours. Drain. Rinse well and drain, squeezing out excess water.
Soak jujube in a small bowl of water for 10 to 15 minutes. Drain, pit, and cut into thin slices.
Combine 1/2 cup water, salted shrimp, scallions, garlic, and ginger in a food processor; puree until smooth.
Pour puree into a large bowl; add jujube, radish, chestnuts, pear, carrots, red chile pepper, green chile pepper, brown sugar, and 2 teaspoon salt. Stir in remaining 5 cups water. Mix in cabbage until well coated.
Pack cabbage mixture into an airtight jar. Pour in any liquid left in the bowl.
Seal and let sit at room temperature until starting to ferment, 1 to 2 days. Transfer to the refrigerator.
