Trim the ends of the lemongrass stalks and bruise them by gently smashing with the back of a knife.
In a large pot, bring the vegetable broth to a boil. Stir in the lemongrass, ginger, garlic, shallots, and chili peppers.
Add the soy sauce, lime juice, and brown sugar. Taste and adjust seasoning as needed.
To make the soup creamier, stir in the optional coconut milk and heat for an additional 2 minutes.