For the stock: In a large pot, place the mushrooms, kombu, spring onions, onions and 3 cups (700 milliliters) water. Bring to a boil over high heat, then reduce the heat to maintain a simmer. Simmer, covered, for 45 minutes. Strain the stock, discarding the solids, and set aside.
For the stew: In a heavy, thick-bottomed medium pot, drizzle in the vegetable oil and warm over low heat. Add the chile flakes and onions and saute over medium-low heat until the onions are just soft, taking care not to brown them. Add the ginger and garlic and give it a quick mix, then pour in the reserved stock. Bring to a simmer over medium-high heat, then stir in the mushrooms, spinach, cabbage and courgette. Bring to a boil, then lower the heat to maintain a simmer. Cook until the vegetables are softened, about 5 minutes. Season with salt. Add the tofu carefully, as it will break apart easily, and simmer until the tofu is heated through. Crack the eggs in on top, give it a gentle mix to break it apart and cook briefly.
Garnish the stew with toasted sesame oil, chives and sliced chiles and spring onions. Serve immediately.
If you aren't a vegetarian, try using clams and clam juice in the broth as they add a great flavor, and start the stew off with a little bit of bacon as well. You can try to find my favorite silken tofu, which comes in a tube, in Korean markets.