Heat the basic soup stock and season it with the soy sauce and salt. Peel the radish and slice it into ½-inch-thick half moons (han gétsu-giri cutting). Peel the carrot and slice it into ¼-inch-thick rounds. Rinse away any white gritty material that may cling to the wedge of bamboo shoot. Slice the shoot lengthwise into ½-inch-thick “combs.” Put the radish, carrot and bamboo-shoot slices into the seasoned stock and cook them, over moderate heat, for 10–12 minutes. Measure the bean paste into a small bowl and pour some of the hot soup over it. Stir to dissolve the paste, then return it to the soup. Remove the soup from the heat while finishing other preparations.
Blanch the chrysanthemum or dandelion leaves in rapidly boiling salted water for 15 seconds, then drain and rinse them under cold water to stop the cooking process. Squeeze out all excess liquid and set aside the green leaves.
Soak the rice cakes in a saucepan of warm water for 5 minutes, then bring the water to a boil. Cook for a minute if necessary to soften further. Pour off the water and transfer a cake to each of 4 deep bowls. (If using freshly pounded rice cakes, do not soak; just place 1 cake directly into each bowl.)
Over each rice cake place a few slices of radish, carrot and bamboo shoot and a few stalks of blanched greens. Stir and heat the soup to barely boiling before pouring some into each bowl. Serve immediately.