In a large pot or Dutch oven, heat the vegetable oil over medium heat.
Add the Thai red curry paste, lemongrass, sliced onion, minced garlic, and galangal (or ginger) to the pot. Sauté for about 3-4 minutes, or until the onions become translucent and fragrant.
Pour in the reduced sodium chicken broth. Stir well to combine all the ingredients, allowing the flavors to meld together.
Add the fish sauce, Asian chili sauce (if using), brown sugar, dried basil, torn kaffir lime leaves (or bay leaves and lime zest), and pepper. Bring the soup to a gentle boil.
Once boiling, reduce the heat to medium-low and add the raw shrimp, sliced white mushrooms, and tomato wedges. Cook for about 5-7 minutes, or until the shrimp turns pink and the mushrooms are tender.
Remove the pot from heat and stir in the lime juice. Adjust seasoning to taste, adding more fish sauce or lime juice if desired.
Ladle the hot soup into serving bowls and garnish with fresh cilantro. Enjoy your vibrant and flavorful Thai Tom Yum Soup!