Cut the salmon fillet into 16 to 20 bite-size pieces. In a small pot, combine the kelp and the water, and bring the water rapidly to a boil. Remove the kelp, and season the broth with rice wine and salt. Poach the salmon pieces in the seasoned broth for only 30 seconds, or until the fish turns opaque. Remove the fish to a platter. Skim the froth from the poaching liquid, and set the broth aside. Wash the broccoli rabe well in cold water, trimming away any leaves that are not bright green. Tie the stalks together in several bunches. In a small pot of boiling water to cover, quickly blanch the broccoli rabe until it is bright green and just barely wilted, about 1 minute. Remove the bunches from the water with tongs or chopsticks, and transfer them immediately to a bowl of cold water. When the rabe is cool, remove it from the water and squeeze out all excess liquid. Cut off the tied stems, keeping the stalks in bundles. Cut the bundles in half lengthwise if they are more than 2 inches long. Stack these bundles of blanched rabe on the same platter as the poached fish pieces.
Cut the cabbage into 1 1/2-inch lengths, and stack these near the blanched rabe. Soak the noodles in warm water for 10 to 15 minutes; drain, and place them on the platter too. Remove the stems from the Shiitake mushrooms, and add the stems to the fish poaching liquid. Gently simmer the broth for 5 minutes, then pick out the stems and discard them. Skim any froth from the broth, and season with the syrupy rice wine. Wipe the caps of the mushrooms with a damp cloth to remove any soil that might be clinging to them. Slice the caps in half diagonally, and set them on the platter with the fish, noodles, and vegetables. Place the fermented bean paste on the platter with the other ingredients. Bring the platter of ingredients to the table if you have a portable cooking unit, and make the bubbling pot there. If not, prepare it in the kitchen and then bring it to the table. Either way, begin by simmering the poached fish and noodles in the broth for 2 to 3 minutes. Add the Shiitake mushrooms, then the broccoli rabe, and simmer another minute or 2. Serve piping hot.