Korean Chicken Soup

Name: Korean Chicken Soup
Ingredients: One 3-pound chicken, neck reserved; 3 1/2 quarts water; 1 medium unpeeled onion, quartered; 2 carrots, scrubbed and cut into 2-inch pieces; 2 celery ribs, cut into 2-inch pieces; 1 large unpeeled garlic clove, smashed; 1 teaspoon whole black peppercorns; 1 large fresh bay leaf; 6 parsley sprigs; 2 thyme sprigs; Kosher salt; 8 ounces thick udon noodles; 2 tablespoons vegetable oil; 1/2 pound shiitake mushrooms, thinly sliced; 1/4 cup finely julienned peeled ginger; One 12-ounce block firm silken tofu, cut into 1/2-inch cubes; 1 cup kimchi, thinly sliced; 2 tablespoons Asian fish sauce; 1 teaspoon Asian sesame oil