Veggie noodle soup and ginger soup

Name: Veggie noodle soup and ginger soup
Cuisine: Asian, Japanese
Ingredients: 4 inches fresh ginger; 2 big cloves garlic; 1 carrot; 6 cups vegetable broth or water; 10 sprigs cilantro*; 8 ounces soba, udon, or rice noodles; 1/4 teaspoon soy sauce or tamari; 1 1/4 cups broccoli cut into bite-size pieces; 1 1/2 teaspoons red miso paste**; 1 carrot, cut into thin matchsticks; 1 cup snow peas cut into matchsticks; 1/3 cup thinly sliced green onions