Make the broth: Add the water, anchovies, and kombu to a large pot. Bring to a simmer over medium heat.
Add the zucchini, carrots, and shiitake mushrooms and cook for 4–5 minutes, until the vegetables are tender. Remove the pot from the heat and set aside.
Make the soup: Meanwhile, bring a medium pot of water to a boil. Add the noodles and cook until tender, about 3 minutes, stirring to keep the noodles from sticking to each other. Rinse the noodles under cold water to stop the cooking process.
Add the cooked noodles to the broth and bring to a boil. Cook for about 1 minute to heat the noodles through.
Ladle the soup into bowls and top with green and red Thai chiles, garlic, soy sauce, salt and pepper.