In a large soup pot, add the chicken stock, lime juice, lemongrass stalks, lime zest, and grated ginger. Bring to a boil over medium heat.
Once it reaches a boil, reduce the heat to low and allow it to simmer for about 20 minutes.
After simmering, carefully remove the lemongrass stalks from the pot. Add in the chicken and oyster mushrooms. Increase the heat to medium, and cook for about 25 minutes.
Pour in the coconut milk, fish sauce, and brown sugar. Stir everything together to combine.
Let the soup simmer for an additional 5 minutes to meld the new flavors.
Serve the soup in large bowls, topping each with a sprinkle of chopped cilantro, lime wedges, and a drizzle of sriracha.