In a soup pot, bring water to a boil and cook the noodles according to package instructions. Drain well and rinse the noodles over cold water. Place half the noodles in each serving bowl, and set aside.
Using the same pot, combine vegetable/mushroom broth and water and bring to a boil. Lower heat, and keep it at a simmer.
While the broth is simmering, heat a wok or a large frying pan over high heat. Once wok is hot, add the oil and swirl to coat. Add garlic and stir for a few seconds.
Then add in ginger and the white part of the scallions. Cook over medium-low heat for a few more seconds to infuse the oil.
Turn heat back up to high, and stir in all the vegetables (including the green parts of the scallions), followed by the Korean chili flakes, soy sauce, and rice vinegar. Cook until the vegetables are slightly softened, about 2-3 minutes.
Turn off heat. Pour the prepared vegetable/mushroom broth into the wok to mix with the vegetables. Lightly season with salt and bring everything to a boil again. Taste and adjust seasoning.
Ladle the hot soup & vegetables over the noodles. Serve immediately. Garnish with leftover scallions.