Japanese Noodle Soup

Name: Japanese Noodle Soup
Ingredients: 1/2 head garlic (6 unseparated cloves); 4 green onions, divided; 2 5-inch pieces dried kombu or kelp; 7 coins sliced fresh ginger (from 2-inch piece); 1/4 cup low-sodium tamari sauce; 3 Tbs. mirin or sake; 2 tsp. sugar, optional; 2 cups thinly sliced shiitake mushrooms; 3 large carrots, thinly sliced; 4 cups (8 oz.) cooked thin rice noodles or udon noodles, or 2 8-oz. pkg. shirataki noodles, rinsed, drained, and snipped into spaghetti-length pieces; 2 cups snow peas and/or thinly sliced napa cabbage; 4 tsp. sesame oil for garnish, optional; 2 tsp. sesame seeds for garnish, optional