Sauté Curry Paste: Heat the vegetable oil in a large pot over medium heat. Add red curry paste and sauté for 1–2 minutes to release the flavors.
Add Broth and Flavorings: Pour in the chicken broth and stir well. Add the lemongrass, galangal (or ginger), kaffir lime leaves, and chili peppers. Let simmer for 5–10 minutes to infuse flavors.
Add Coconut Milk & Seasonings: Stir in the coconut milk, fish sauce, soy sauce (if using), and brown sugar. Let it come back to a simmer.
Add Mushrooms and Shrimp: Add mushrooms and cook for about 3 minutes. Then add the shrimp and cook just until pink and opaque (about 2–3 minutes).
Finish with Lime Juice: Turn off the heat. Stir in lime juice to taste.
Serve: Ladle into bowls and garnish with fresh cilantro, Thai basil, and extra chili if desired. Serve with lime wedges on the side.