Tom Kha Gai (Thai Chicken Soup with Coconut and Galangal)

Name: Tom Kha Gai (Thai Chicken Soup with Coconut and Galangal)
Prep time: 10 min
Cook time: 20 min
Total time: 30 min
Cuisine: Thai
Ingredients: 1 cup (240ml) homemade or store-bought chicken stock (see note); One 4-inch piece fresh galangal (50g), peeled; 2 2/3 cups (620ml) homemade or store-bought chicken stock (see note); One 4-inch piece fresh galangal (50g), peeled and thinly sliced; 3 stalks lemongrass, bottom 7 inches only, outer leaves discarded, tender core cut on a bias into 2-inch lengths (about 120g); 2 shallots (40g), peeled and roughly smashed in a mortar and pestle; 1/4 cup (60ml) fish sauce, divided; 1 1/2 pounds (680g) boneless, skinless chicken thighs, cut into 1 1/2-inch cubes; 10 fresh or frozen makrut lime leaves (4g), middle ribs removed; 5 to 9 fresh Thai red chiles (5g to 9g total), stemmed and lightly smashed; 1 cup (240ml) full-fat coconut cream, such as Aroy-D (see note); 1/4 cup (60ml) fresh lime juice from 2 limes; Cilantro leaves, for garnishing