Prepare the noodles according to package directions. OR bring a large pot of water to a boil. Add the noodles and let cook for about 5 minutes. The noodles should be al dente. If you cook it for too long, it will be too mushy. Drain and rinse the noodles under cold running water. Divide the noodles equally among 4 large soup bowls. Set aside.
In the same large pot, add 7 cups of water. Rinse the piece of kombu and add it to the pot a long with about 25 dried anchovies. Over high heat, bring the water to a boil. Lower the heat to medium, cover, and let simmer for about 20 minutes. Remove the kombu and scoop out the anchovies with a strainer or a slotted spoon. Discard the kombu and anchovies.
Add the dwaenjang, kochujang, red pepper powder, and a pinch of salt to the broth. Stir to dissolve the pastes. Add the zucchini, daikon, mushrooms. Raise the heat and bring to a boil. Lower the heat to medium again and let simmer for about 10 minutes.
Add the monkfish to the broth and simmer until the fish is cooked through or for about 15 minutes.
To serve, ladle the soup over the noodles. Garnish with the sliced green onions. Serve hot!