Heat oil. Once the oil is hot, add onions and garlic and saute for a minute.
Add lemongrass stalks, galangal, Thai red chilies, kaffir lime leaves, and vegetable stock, and bring the soup to a boil.
Reduce the heat to low. Cover the pan with a lid and let the soup simmer for 25-30 minutes.
Using a strainer, remove the onions, lemongrass, galangal, kaffir leaves, and chilies.
Add mushroom to the soup and cook for 3-4 minutes.
Add fish sauce, brown sugar, lemon juice, and coconut milk, and bring the soup to a simmer, stirring frequently. Garnish with cilantro, chopped red chilies, and lemon wedges, and serve hot.