Prepare Shrimp and Stock: Peel the shrimp, reserving the heads and shells for stock. Toast the heads and shells with a touch of neutral oil, then add water and simmer to make shrimp stock.
Simmer Ingredients: To the strained shrimp stock, add lemongrass, lime leaves, galangal, and Thai chilis. Simmer to infuse flavors.
Finish the Soup: Add the shrimp to the simmering broth. After a brief cook, remove from heat and season with chili paste, fish sauce, and lime juice to taste.