Pull the heads off the shrimp and place them in a wok or large skillet. Peel and clean the shrimp and set aside. *You can add the shrimp shells to the skillet as well, but the heads are the important part.
Add the oil to the skillet and set over medium heat. Add a good pinch of salt. Sauté the shrimp heads to release their flavor into the oil, cooking until they are red and crispy. Then turn off the heat.
Meanwhile, trim the tips and root ends of the lemongrass stalks and remove the tough outer layers. Cut the lemongrass into 1 ½ inch segments. Cut the galangal into 3 or 4 pieces.
Using a meat mallet or the side of a knife, smash the lemongrass, kaffir lime leaves, onion, chilies, and galangal. Place them in a medium soup pot. Pour the water into the pot then bring to a boil. Reduce the heat and simmer for 5-10 minutes, until the broth smells bright and fragrant.
Remove and discard any tough sections of lemongrass. (Keep them all in if the stalks are soft.) Increase the heat to high. Stir in the mushrooms. Boil for 1 minute. Then stir in the shrimp and fish sauce, cooking until the shrimp are just cooked through, about 45 seconds.
Turn off the heat and stir in the lime juice. Then stir in 3-4 tablespoons of the shrimp oil. (Discard the heads; do not add them to the soup.)
Serve with fresh lime wedges and cilantro. Tom Yum is often served over rice, however it’s low carb served as-is!
Tom Yum is sometimes made with coconut milk. You can add a splash of coconut milk to the soup if you like, at the end.