Boil 2 ½ cups of water in a pot over medium heat.
While waiting for the water to boil, take the stalks of lemongrass, chop the roots off and discard along with the outermost leaf of each stalk. Then, cut every stalk into 1-inch strips.
Hand-tear the kaffir lime leaves.
Thinly slice the galangal root.
Peel the shallots and cut them in half.
Gently pound the lemongrass, galangal, shallots in a mortar and add them to the pot and boil for about 10 minutes (This will allow the herbs to release fragrance and infuse the base of your soup).
Pound the chilies in a mortar or smash them on the cutting board with the back of your knife.
Cut the tomato into wedges and the mushrooms in half. Roughly chop the culantro.
Add the tomato wedges to the pot.
Prepare your shrimp. Peel the shell, and remove the head but keep the tail on. Then, devein and rinse.
Once the water is boiling, add the mushrooms and shrimp to the pot and cook for 2-3 minutes or so.
Add the fish sauce, sugar, and Thai chili oil.
Taste test the tom yum and adjust the flavor as needed before adding the kaffir lime leaves and turning off the heat.
Add the lime juice and taste test again and adjust as needed.
Transfer the soup to a serving bowl, sprinkle with the chopped culantro.