Tom Yum Soup (Tom Yum Goong)

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1. 1Step 1: Place the shrimp heads and shells in a stock pot along with the oil and the daikon and/or onion, if using. Sauté over medium-high heat, pressing with a spatula to release the tomalley from the shrimp heads.
2. 2Step 2: When the bits stuck to the bottom of the pot begin to brown and smell like grilled shrimp, deglaze with water and scrape up all the browned bits. Bring to a simmer and cook for 5 minutes.
3. 3Step 3: Using a wire skimmer, remove and discard the shrimp shells. (Small bits of vegetables can remain.) Measure the stock; you need 4 cups (960 ml) for the next step. If you're short, top up with water; if you have a little extra, that's fine.
4. 4Step 4: Add the stock, lemongrass, galangal, chilies, and mushrooms to the pot. Bruise the lime leaves by twisting them in your hands, then tear them into chunks, discarding the central ribs, and add to the pot. Bring to a simmer and simmer for about 5 minutes. (Note: These herbs are traditionally left in the soup as garnish but are not meant to be eaten; inform your guests not to eat them or remove them after infusing.)
5. 5Step 5: Turn up the heat to bring the soup to a boil. Ladle some broth into the Thai chili paste, stir to loosen, then pour it into the soup. Add the fish sauce and the shrimp. Cook the shrimp until they're halfway done, 30-50 seconds depending on size, then turn off the heat and let the residual heat finish cooking them, about another minute.
6. 6Step 6: Stir in the lime juice and taste; adjust seasoning if needed. The soup should lead with sour, but with enough sweetness to balance. If too sour, add the sugar.
7. 7Step 7: Stir in the cilantro leaves and serve with jasmine rice on the side or in the soup, as you prefer.