Thai Coconut Chicken Soup

Name: Thai Coconut Chicken Soup
Ingredients: 1 whole free-range chicken (about 3 1/2 pounds), rinsed, giblets discarded; 2 carrots, cut in large chunks; 3 celery stalks, cut in large chunks; 2 large white onions, quartered; 1 head of garlic, halved; 1 turnip, halved; 1/4 bunch fresh thyme leaves; 2 bay leaves; 1 teaspoon whole black peppercorns; 3 kaffir lime leaves, fresh or dried, hand torn; 2 small Thai chiles, halved lengthwise; 2 cloves garlic, crushed; One 3-inch piece fresh ginger, peeled and cut into 4 chunks; 1 stalk lemongrass (white part only), cracked open with the flat side of a knife; 1 1/2 cups shredded cooked chicken; One 13-ounce can unsweetened coconut milk; One 8-ounce can straw mushrooms, rinsed; 2 tablespoons Thai fish sauce (nam pla); 1 1/2 teaspoons sugar; Juice of 4 limes; Kosher salt and freshly ground black pepper; 1/4 cup chopped fresh cilantro leaves, for garnish