Chop all the vegetables and tofu according to the instructions above in the ingredients list, and set aside.
Prepare all the stir fry ingredients and set aside. The key is to have all your ingredients ready and available at hand before the stir frying begins because things will move very quickly once the fire is on.
Heat a well-seasoned, large wok or a large, deep non-stick pan over high heat with about 2 tablespoons of oil. Add tofu and stir fry until golden. Once the tofu is golden, add mushrooms and stir fry until the mushrooms are golden.
Move the tofu and mushrooms off to one side of the pan. Add 1-2 tablespoons of oil to the other side and add minced ginger. Stir fry the ginger in oil for about 15 seconds to infuse the oil with the ginger flavor. Add carrots and cabbage and stir fry everything together for about 1-2 minutes. Sprinkle over all of the gochugaru and smoked paprika. Stir fry for about 15 seconds. Add tamari or soy sauce around the pan and stir fry for another 10 seconds, then quickly pour in the kombu dashi along with the kelp. (If you soaked the kombu dashi overnight, then only pour the liquid and discard the kelp.) Turn the heat down to medium heat. Add mushroom seasoning, rice vinegar, and black pepper. Remove the kelp just before the water comes to a boil. When you start to see tiny bubbles forming on the surface, take the kelp out. You don’t want to boil the kelp as it can lose some of its umami flavor from overheating. Simmer the soup for about 15-20 minutes. Meanwhile, prepare the noodles.
Once the soup has been simmering for about 15-20 minutes, stir in bok choy and mung bean sprouts. Cook for about 30 seconds to 1 minute. Season the soup to taste with salt. Ladle the soup over the noodles and serve immediately.