Prepare the Shrimp Broth: Heat the neutral oil in a medium pot over medium heat. Add the shrimp heads and shells, stirring occasionally until they turn pink and release their aroma, about 3–4 minutes. Pour in the water, then add the diced daikon and onion if using. Bring to a gentle simmer, cooking for 8 to 10 minutes to extract rich flavors. Strain the broth through a fine mesh sieve, discarding solids, and set the clear stock aside.
Infuse the Broth with Aromatics: Return the shrimp or chicken broth to the pot and add the smashed lemongrass pieces, kaffir lime leaves, and galangal slices. Simmer gently for 5 minutes, allowing the broth to soak up the fragrant herbal notes.
Add Mushrooms and Chilies: Stir in the torn oyster mushrooms and the prepared chili paste along with the minced or pounded Thai chilies. Allow the soup to simmer for an additional 3 minutes, which helps meld the flavors together.
Cook the Shrimp: Add the whole shrimp to the broth. Simmer just until they turn pink and curl, about 2–3 minutes. Avoid overcooking to maintain their tender texture.
Final Seasoning: Remove the pot from heat and stir in the fish sauce, fresh lime juice, and sugar. Taste and adjust seasoning, balancing sour, salty, sweet, and spicy flavors to your preference.
Serve and Garnish: Ladle the hot soup into bowls, garnishing with chopped cilantro or sawtooth coriander. Serve immediately with jasmine rice on the side for a complete meal.