Heat oil in a large pot over medium heat. Add mushrooms and cook until soft, about 5 minutes.
Add lemongrass, ginger, garlic, and chilies. Stir-fry for 2 minutes until fragrant.
Pour in the broth and bring to a boil. Reduce heat and simmer for 10 minutes.
Add fish sauce (or soy sauce), lime juice, and sugar. Adjust seasoning to taste.
If using tofu or chicken, add it to the soup and cook until heated through (5 minutes).
Remove from heat, discard lemongrass and ginger slices, and serve hot.
Garnish with cilantro and lime wedges.