Tom Kha Gai (Chicken Coconut Soup)

Name: Tom Kha Gai (Chicken Coconut Soup)
Cuisine: Asian, Thai
Ingredients: 2 stalks fresh lemongrass, tough outer layers removed; 1 1" piece ginger, peeled; 10 makrut lime leaves, or use 1 tablespoon lime zest and 1/4 cup lime juice; 6 cups low-sodium chicken broth; 1 1/2 pounds skinless, boneless chicken thighs, cut into 1" pieces; 8 ounces shiitake, oyster, or maitake mushrooms, stemmed, caps cut into bite-size pieces; 1 13.5-ounce can coconut milk; 2 tablespoons fish sauce; 1 teaspoon sugar; Chili oil, cilantro leaves with tender stems, and lime wedges (for serving); Cilantro leaves with tender stems; Lime wedges