Trim off the top third and very bottom of the lemongrass stalks. Using the side of a knife, press down across the stalks to bruise the lemongrass and release the oils. Chop each stalk into 4 pieces and set aside.
Add the chili peppers, garlic, and galangal to a mortar and pestle and grind into a paste. Set aside.
Melt the coconut oil in a large pot over medium heat. Once the oil begins to shimmer, add the lemongrass and cook for 3-4 minutes, until fragrant. Add the chili pepper paste and cook for another 3-4 minutes, until fragrant.
Add the vegetable broth, tomato, lime leaves, coconut milk, and soy sauce and stir to combine. Bring to a boil. Cover, then reduce the heat to low and simmer for 20 minutes, until broth has reduced slightly.
Add the tofu and mushrooms and stir to combine. Cook for 5 minutes, until the mushrooms are tender.
Add the lime juice and agave and stir to combine. Season with salt to taste.