In a large pot, combine the vegetable or chicken broth and coconut milk. Bring it to a gentle simmer over medium heat.
Add the lemongrass stalks, Thai chili peppers, galangal, and kaffir lime leaves to the pot. Let the mixture simmer for about 10 minutes to allow the flavors to infuse.
Stir in the mushrooms and tomatoes, and continue to simmer for another 5 minutes until the mushrooms are tender.
Add the fish sauce and fresh lime juice to the soup. Taste and adjust the seasoning with salt, if needed.
Remove the pot from heat and discard the lemongrass stalks, galangal, and kaffir lime leaves.
Ladle the soup into bowls and garnish with cilantro and Thai basil leaves.
Serve hot and enjoy the vibrant flavors of Spicy Thai Lemongrass Soup.