Place a heavy bottom pan on medium heat and then add vegetable broth, coconut milk, cut lemongrass and slices of galangal to it.
Let it come to a slow simmer, you do not want to boil the milk here. Let it heat through for 5 minutes.
Then add in the veggies-carrots, mushroom, pepper and stir.
Also add the kaffir lime leaves. Remember to tear/crush them before adding to the soup. That's what brings out their flavor.
Add thai chilies as well. If you like spicy food, add more of the chilies. I like mine to be on the milder side.
Let the veggies simmer for around 6 to 7 minutes, then add the salt.
Also add the sugar (if using, I recommend it) and mix. Turn heat to low and simmer for 3 more minutes and then remove pot from heat.
Stir in the chopped cilantro and mix.
Finally add in lime juice. Taste test and adjust spice level and salt to taste at this point.
Discard lemongrass, galangal and serve vegan tom kha with more cilantro and a lime wedge.
