In a small pan, bring 2 cups of water and the mushrooms to a boil. Remove from heat and soak for 15-20 minutes until softened. Strain the soaking liquid into a 2 quart pot and set the shiitake mushrooms aside.
Add the remaining 4 cups water, scallions, carrots, radish, and ginger to the soaking liquid.
Cover, bring to a simmer and cook gently for about 30 minutes. Strain and return the stock to the soup pot.
While the stock is simmering, heat oil in a heavy skillet(or wok) and add the onions. Cook on medium heat for 15 minutes, stirring frequently, until the onions are browned well(don't burn!). Add the garlic and saute for 3 minutes.
Mix in ginger, cabbage, and carrots. Cook, stir often until cabbage is limp and crisp tender, about 10 minutes. Add the veggies to the strained stock and stir in the chili paste and soy sauce.
Remove and discard the shiitake stems. Thinly slice the caps, add them to the soup, and reheat until just boiling.
Ladle the soup into bowls. Top with the hijiki seaweed or scallions, or both. Enjoy!